Characterization of the Structural Morphology of Chemically Modified

Article pubs.acs.org/Langmuir

Characterization of the Structural Morphology of Chemically Modified Silica Prepared by Surface Polymerization of a Mixture of Long and Short Alkyl Chains Using 13C and 29Si NMR Spectroscopy Hafeez O. Fatunmbi† and Martha D. Bruch*,‡ †

Separation Methods Technologies, Inc., 31 Blue Hen Drive, Newark, Delaware 19713, United States Chemistry Department, Oswego State University, Oswego, New York 13126, United States

‡

ABSTRACT: A series of bonded phases were prepared by the chemical modification of silica using the surface polymerization of trifunctional and difunctional ligands, and the structural morphology was characterized by solid-state nuclear magnetic resonance (NMR) spectroscopy using cross-polarization and magic angle spinning (CP/MAS). Mixed-phase surfaces were prepared using mixtures of trifunctional long-chain (C18) ligands with trifunctional and difunctional short-chain (C1) ligands, and these surfaces were compared to the corresponding single-phase surfaces consisting of only long- or short-chain ligands. For both types of mixed-phase surfaces, the incorporation of short chains increases the overall ligand density, the density of long chains, and the degree of cross-linking between ligands compared to that of the single-phase surface consisting exclusively of long chains. When the percentage of long-chain ligands in the mixture is high, a horizontally polymerized monolayer of chains is formed on the silica surface for both trifunctional and difunctional short chains. However, essentially all of the long chains adopt a trans conformation when trifunctional short chains are used, and a significant number of gauche defects are observed for the long chains when mixed with difunctional short chains. Furthermore, the ligands on the mixed-phase surface are more rigid when the short chains are trifunctional. When the percentage of trifunctional short chains is increased, some vertical polymerization occurs, caused by the molecular stacking of the highly reactive short chains near the surface. However, this does not preclude cross-linking between the ligands necessary to seal the surface, and the degree of cross-linking is quite high, suggesting that the short chains cross-link both vertically, away from the surface, and horizontally, across the surface. No such vertical polymerization is observed for the bulkier difunctional short chains. For both trifunctional and difunctional short chains, the surface chains are more mobile, with a greater number of gauche conformations among the long chains when the percentage of short-chain ligands in the reaction mixture is increased.

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INTRODUCTION Stationary phases used in high-pressure liquid chromatography (HPLC) columns are typically prepared by chemical modification of the surface of silica, resulting in covalent bonding of alkyl chains to surface silanols. This is typically done by reacting chlorosilanes with silica gel, called the substrate. The details of the structure of the bonded phase formed on the surface can dramatically affect the retention time of solutes carried through the column containing the stationary phase by the mobile phase.1−7 The density, length, conformation, mobility, and spacing of the alkyl chains on the surface can affect the interactions between the solute and the stationary phase as the mobile phase flows through the column, and subtle differences in these surface interactions can change the performance of the column in terms of both the ability to separate solutes with similar chemical structures and the longevity of the column. However, despite considerable study, the relationship between the method used for chemical modification and the structural detail of the resultant surface is not fully understood. To be useful for chromatographic applications, the chemical modification process should produce a surface that is reproducible and remains largely unchanged © 2013 American Chemical Society

after repeated exposure to solvents used in the mobile phase. Both the reproducibility and stability of the surface depend upon the structural morphology of the bonded phase. Unreacted silanols can cause a surface to degrade over time, especially under basic or acidic conditions,8,9 so it is desirable to minimize the number of surface silanols in order to increase the stability of the bonded phase. Because the reaction of chlorosilanes with the silica substrate results in the formation of covalent bonds with the substrate, the chlorosilanes are not technically ligands. However, they are commonly referred to as ligands because they are attached to the surface of the silica, and this terminology will be used to facilitate a discussion of the chemically modified surfaces. The number of chlorines attached to the silicon at the end of the alkyl chain in the ligand determines the number of bonds that can be formed by the ligand, either by direct attachment to silanols on the silica surface or by water-assisted condensation reactions to form bonds between adjacent ligands. Ligands Received: October 15, 2012 Revised: March 25, 2013 Published: March 26, 2013 4974

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containing a mixture of long-chain (C18) and short-chain (C1) ligands using surface polymerization methods. First, two surfaces with a different ratio of trifunctional long chains to trifunctional short chains were prepared to see the effect of varying the ratio of long to short chains on the structural morphology of the resultant bonded phase. Then two surfaces were prepared using different ratios of trifunctional long chains and difunctional short chains to determine the effect of the functionality of the short chains on the structure formed on the surface. Finally, the structures formed on these mixed-phase surfaces were compared to those formed on the corresponding single-phase surfaces. The mixed-phase and single-phase surfaces were analyzed by nuclear magnetic resonance (NMR) spectroscopy using crosspolarization and magic angle spinning (CP/MAS), a powerful method for probing the structural morphology of the surface. However, quantitative data cannot be obtained from 13C NMR CP/MAS spectra using a single contact time because differing mobility between the long and short chains as well as mobility differences within the long chains can cause significant differences in the efficiency of cross-polarization, leading to intensity distortions.13−16 This problem was overcome by obtaining spectra at a series of contact times and fitting the data to a double-exponential function in order to extract equilibrium intensities, undistorted by mobility differences.12,14,15 The relative number of long and short chains in the bonded phase was determined from variable contact time 13C data, enabling a direct comparison between the ratio of long and short chains in the reaction mixture and the ratio actually incorporated into the bonded phase. This information, in combination with the mass percent carbon obtained from elemental analysis, was used to calculate the density of chains on the surface of the silica, revealing the effect of short chains on the overall surface coverage for the mixed phases. Furthermore, 13C NMR spectra provide insight into the chain conformation because separate signals are observed for trans and gauche conformations.6,7,13,17,18 The percentage of long chains in trans and gauche conformations was determined from the 13C spectra, and results for the different mixed-phase surfaces are compared. The effect of chain density and ligand functionality on the mobility of the attached chains was also investigated using the 13 C NMR data. In addition to providing quantitative peak intensities, variable contact time 13C data were used to obtain an estimate of the proton spin−lattice relaxation time in the rotating frame, T1ρ.12,14,15 This relaxation time depends on the mobility of the alkyl chains, so a comparison of relaxation times between chains on different surfaces provides insight into their relative mobility.6,7,13−15,19−21 Because clusters of long chains are less mobile than isolated chains, relaxation times are an indirect measure of chain packing. Although 13C NMR provides a direct probe of the ligands attached to the surface, complementary information can be obtained by using 29Si CP/MAS NMR to examine the effect of the ligand on the substrate. 29Si NMR enables the observation of the surface silicon atoms, with different signals observed for silicons with different attached structural groups.4−7,12,19,22−25 To understand how the relative number of long and short chains affects the cross-linking in the polymeric network of chains on the surface, 29Si NMR was used to compare the degree of cross-linking observed between surfaces containing differing numbers of long- and short-chain ligands for both triand difunctional short chains. Because difunctional short chains

containing one, two, or three chlorines are referred to as monofunctional, difunctional, and trifunctional ligands, respectively. Monofunctional ligands, which have only one point of attachment with the surface, can react with only a fraction of the available silanols because of steric hindrance, leaving a significant number of unreacted silanols exposed to the surface.10 The conventional remedy to this problem employs an end-capping method where a smaller, short-chained, monofunctional compound (e.g., chloro(trimethyl)silane) is allowed to react further with the silica surface that has already been modified. These smaller monofunctional ligands have greater access to the surface than the corresponding long chains, so they consume some of the surface silanols that remain unreacted after the initial modification. Even when this remedy is exhaustively performed, previous studies showed that 50% or more of the surface silanols are still unreacted.4 The number of unreacted silanols exposed to the surface can be minimized through the use of difunctional or trifunctional ligands containing two and three reactive chlorines, respectively. In addition to forming bonds to the silica surface, these ligands can form bonds with each other, resulting in cross-links between adjacent ligands, and this creates a polymeric network of ligands on the silica surface. The formation of a polymeric network results in fewer unreacted silanols on the surface compared to surfaces formed from monofunctional ligands.1,5,11 Furthermore, silanols originally on the surface that remain unreacted are generally covered up by the ligand network, so they are no longer exposed to the surface. Solution polymerization methods, where water is added to a reaction slurry of trifunctional silane ligands and silica, can result in nonuniform polymeric surfaces containing clusters of ligands in some locations and few ligands on other spots on the surface.11 A more regular surface with higher coverage can be obtained using surface polymerization, where trifunctional silane ligands are allowed to react on a humidified surface. Water available at the surface potentially enables trifunctional ligands to form two cross-links to adjacent ligands via a condensation reaction in addition to bonding to the surface. Surface polymerization using trifunctional C18 ligand Cl3Si(CH2)17CH3 has been shown to result in HPLC stationary phases with superior stability compared to that of monomeric surfaces prepared using monofunctional C18 ligand Cl(CH3)2Si(CH2)17CH3, especially under acidic or basic conditions.1,4 However, when only long chains such as C18 are used, steric crowding limits the number of chains that can reach the surface to react, limiting both the coverage and the degree of cross-linking that can be obtained in the bonded phase.5 Hence, unreacted silanols remain on the surface along with secondary silanols created by the surface polymerization process. The degree of cross-linking can be increased by using a mixture of long and short chains to form the bonded phase.5,12 Fatunmbi and co-workers have shown that a mixture of C18 and C3 carbon chains produces a self-assembled monolayer with more extensive cross-linking than if only C18 chains are used,4,12 and the degree of cross-linking increases further when C1 chains are used in place of C3 as the short chains.5 However, the effect of changing the ratio of long to short chains on the chain density and degree of cross-linking has not been investigated. Furthermore, the effect on the surface structure of using difunctional short chains instead of trifunctional short chains in a mixture with trifunctional long-chain ligands in a surface polymerization process is not known. We report here the synthesis and characterization of a series of bonded phases 4975

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reaction, and the mixture was stirred with humidified silica at room temperature for 8 h. Three different single-phase surfaces were prepared by reacting stoichiometric quantities of trichloro(octadecyl)silane (Gelest, Inc., CAS no. 112-04-9, d = 0.984 g/mL), dichlorodimethylsilane (Gelest, Inc., CAS no. 75-78-5, d = 1.07 g/mL), and trichloro(methyl)silane (Gelest, Inc., CAS no. 75-79-6, d = 1.27 g/mL) with humidified silica particles under anhydrous conditions, except for a layer of water on the silica substrate formed during the humidification process. These singlephase surfaces are designated as SL (long chain), SD (difunctional short chain), and ST (trifunctional short chain) respectively. Mixedphase surfaces were prepared by mixing stoichiometric quantities of long-chain octadecyl (C18) ligands with the Cl3Si(CH2)17CH3 structure and short-chain methyl (C1) ligands with the Cl3SiCH3 or Cl2Si(CH3)2 structure in long-chain/short-chain ratios of 4:1 and 1:1 by volume and then reaction with the humidified silica as described above. The mixed-phase surfaces prepared with trifunctional shortchain ligands are designated as MT-4 (4:1 long/short-chain ratio) and MT-1 (1:1 ratio) whereas those prepared with difunctional short-chain ligands are designated as MD-4 (4:1 ratio) and MD-1 (1:1 ratio). For all surfaces, the reaction was performed under nitrogen and with ultradry heptane solvent. After the reaction, the bonded phase was rinsed thoroughly in heptane and dried at 120 °C for 1 h. The reactions used to make the various surfaces on humidified silica are shown in Figure 1. The various bonded phases are summarized in Table 1; the mole percent of long and short chains was calculated from the volume ratios using the densities and molar masses of the three types of ligands. Elemental Analysis. All samples were submitted to an independent laboratory (Microanalysis, Inc., Wilmington, DE) for the determination of the percent carbon (single trial per sample). NMR Spectroscopy. All NMR spectra were obtained on a Bruker Avance 300 MHz NMR (7 T magnet) using a combination of crosspolarization and magic angle spinning (CP/MAS).15 Samples were packed into a 7 mm zirconium rotor and were spun at the magic angle at a frequency of approximately 3.5 kHz. For 13C spectra (75.5 MHz), 2048 transients were acquired over a spectral width of 30 kHz using a 2 s relaxation delay with contact times ranging from 0.05 to 15 ms. For 29 Si spectra (62.9 MHz), 5000 transients were acquired over a spectral width of 15 kHz using a 2 s relaxation delay with a contact time of 5 ms. For each transient, 1486 data points were acquired for 29Si and 1804 points were acquired for 13C, and all spectra were zero-filled to 32 768 points prior to Fourier transformation. A shaped (ramped) pulse was used with an effective 90° pulse width of 4.5 μs for 13C and 5.6 μs for 29Si. This corresponds to a spin-lock field of 55 kHz for 13C and 45 kHz for 29Si. Spectra were processed using an exponential apodization function using line broadening of 10 Hz for 13C spectra and 20 Hz for 29Si spectra. 29Si spectra were referenced externally to a chemical shift of 0 ppm for 2,2-dimethyl-2-silapentane-5-sulfonic acid (DSS), and 13C spectra were referenced externally to a chemical shift of 17.4 ppm for the methyl signal in hexamethyl benzene (HMB). The sample mass was determined by the difference between the full and empty rotors. The mass of silica for each sample was obtained by subtracting the mass of the attached ligands from the sample mass, where the mass of the attached ligands was calculated from the percent carbon determined from microanalysis. Each trifunctional long chain was assumed to contribute a mass corresponding to C18H37O2Si for chains in T3 structures and C18H37O3Si otherwise. Similarly, each trifunctional short chain was assumed to contribute a mass corresponding to (CH3)2O2Si for T3 structures and CH3O3Si otherwise. Difunctional short chains were assumed to contribute a mass corresponding to C2H6OSi because all attached difunctional ligands were determined to be in D2 structures. (See the Results section for definitions of T3 and D2 structures.)

are bulkier and have fewer reaction sites than trifunctional short-chain ligands, difunctional short chains are expected to be less effective at forming 2D cross-linking networks. For mixedphase surfaces prepared using trifunctional short chains, only the total cross-linking for both long and short chains could be measured. However, silicon sites with attached difunctional ligands have different chemical shifts compared to silicons with attached trifunctional ligands,10,17 which allows the degree of cross-linking associated with the short chains to be measured separately from that for long chains in the 29Si NMR spectrum. The amount of cross-linking in the mixed-phase surfaces was compared to that observed on the single-phase surfaces consisting of exclusively long or short chains. The ligand densities obtained from 13C NMR and elemental analysis, in combination with the degree of cross-linking obtained from 29Si NMR, provide insights into the nature of the polymeric network formed on the surface. The ultimate goal of the chemical modification of silica using surface polymerization techniques is to obtain horizontal polymerization of the ligands, where the connections between adjacent ligands extend out horizontally over the surface, creating a uniform monolayer of ligands that are chemically bonded both to the surface and to each other. This is achieved by limiting the water content and restricting the available water to the surface of the silica substrate. However, the exact amount of water needed at the surface to achieve horizontal polymerization is not known. Too little water can result in incomplete polymerization, leaving unreacted chlorines remaining on the attached ligands.25 However, too much water has the potential to enable vertical polymerization, where one ligand initially attaches to the substrate surface and subsequent ligands attach to the anchored ligand, without forming a separate bond to the substrate. This creates a polymeric chain of ligands that extends up vertically from the surface instead of the desired horizontal polymerization across the substrate surface. The amount of water needed to facilitate vertical polymerization may depend on the size, reactivity, and functionality of the ligands used to create the polymeric network. For this study, the water content of the silica prior to reaction was carefully controlled by humidifying the silica to 50% relative humidity. The nature of the polymerization (vertical versus horizontal) was determined by 13 C and 29Si NMR data, and the results for the different singlephase and mixed-phase surfaces are compared to each other and to mixed-phase surfaces prepared using the same protocol that were analyzed previously by NMR.12

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EXPERIMENTAL SECTION

Synthesis of Bonded Phases. The synthesis of self-assembled monolayers is well established, and the details have been published previously.5,12 All samples were prepared using silica (Separation Methods Technologies, Inc., SMT-silica, catalog no. BS-5-60) with a pore size of 60 Å, a particle size of 5 μm, and a surface area of 500 m2/ g. BS-5-60 silica is very pure with insignificant traces of metal impurities. To prepare the surface, typically 2 g of the silica gel was first dried by heating to 120 °C under a stream of nitrogen for 2 h. The silica and a dish of about 2 g of deionized water were placed in a specially built chamber (Terra Universal, with a relief/bleed valve) initially purged with nitrogen. The humidity of the chamber was monitored using a Cole Parmer thermohygrometer (catalog no. 37950-00). The percent humidity usually rose from an initial value of about 1%. The humidified silica was pulled out for immediate reaction with the ligands when a percent humidity of 50% was measured on the meter, typically within 3 h of exposure to water vapor in the chamber. The total volume mixture of 2 mL of the silane was used in each

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RESULTS C NMR. Three surfaces were prepared using exclusively one type of ligand: trifunctional long chains (SL), trifunctional short chains (ST), and difunctional long chains (SD). The 13C

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Figure 2. 13C CP/MAS NMR spectra at a contact time of 2 ms. (a) Surface SL, (b) surface ST, and (c) surface SD.

expected, with the signal for the methyl group shifted upfield when trifunctional ligands are used (ST) compared to difunctional ligands (SD). The ligand density was calculated from the percent carbon, the carbon chain length and molar mass of the attached ligand, and the surface area of the silica using eq 1,3 and the results are summarized in Table 2. density = (wt % C × 106)(surface area) (1200)(chain length) − (wt % C)(chain molar mass)

Figure 1. Preparation of single-phase and mixed-phase surfaces on humidified silica gel. (a) Surface SL. (b) Surface ST. (c) Surface SD. (d) Surfaces MT-4 and MT-1 where R = −CH3 or −(CH2)17CH3 and R′ = H, −SiCH3, or −Si(CH2)17CH3. The ratio x/y = 4:1 by volume (mole ratio 1.2:1) for surface MT-4 and 1:1 by volume (mole ratio 0.3:1) for surface MT-1. (e) Surfaces MD-4 and MD-1 where R and R′ both are −CH3 or R = −(CH2)17CH3 and R′ = OH, −O− Si(CH2)17CH3, or −O−Si(CH3)2 The ratio x/y = 4:1 by volume (mole ratio 1.2:1) for surface MD-4 and 1:1 by volume (mole ratio 0.3:1) for surface MD-1.

(1)

The observed density of 5.3 μmol/m2 is typical for polymeric C18 bonded phases5,6,11,12 and is less than the density of approximately 8.0 μmol/m2 expected for a monolayer of chains on the surface,6,26 indicating incomplete coverage of the surface. Greater coverage was achieved when only difunctional short-chain ligands were used (SD). For surface SD, the density of chains calculated from the percent carbon (eq 1) is indicative of monolayer coverage of the surface. Difunctional ligands can form only two bonds, either to the surface or to adjacent ligands, compared to three bonds for trifunctional ligands, so fewer cross-links to other ligands are possible. The ligand density determined for surface SD indicates that despite the reduced cross-linking ability of difunctional ligands compared to that for trifunctional ligands, short chains have less steric hindrance than long chains, enabling greater ligand density on surface SD compared to that on surface SL. Surface polymerization using exclusively trifunctional short chains resulted in an extremely high ligand density, indicating that the surface coverage exceeded a monolayer. Four mixed-phase samples were prepared where trifunctional long and either trifunctional or difunctional short chains were allowed to react with the surface simultaneously. This creates a network containing a mixture of long and short chains attached to the surface, where some of the ligands are connected to each other via cross-links. For both trifunctional and difunctional short chains, a pair of bonded phases was prepared (four different mixed-phase surfaces total), with differing ratios of

Table 1. Composition of Various Prepared Bonded Phases

designation

long-chain structure

short-chain structure

long-/shortchain ratio (v/v) in the reaction mixture

SL ST SD MT-4 MT-1 MD-4 MD-1

Cl3Si(CH2)17CH3 none none Cl3Si(CH2)17CH3 Cl3Si(CH2)17CH3 Cl3Si(CH2)17CH3 Cl3Si(CH2)17CH3

none Cl3SiCH3 Cl2Si(CH3)2 Cl3SiCH3 Cl3SiCH3 Cl2Si(CH3)2 Cl2Si(CH3)2

N/A N/A N/A 4:1 1:1 4:1 1:1

mol % long chain in the reaction mixture 100 0 0 55 23 55 24

spectrum of the single-phase surface composed exclusively of long chains (SL) shows three signals as expected, with assignments indicated on the spectrum (Figure 2a). The 13C spectra of the single-phase surfaces composed exclusively of short chains (Figure 2b,c) each contain only one signal as 4977

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Table 2. Summary of Quantitative Results from 13C NMR Variable Contact Time Data sample

% carbon

% C18 chains

total density (μmol/m2)

SL ST SD MT-4 MT-1 MD-4 MD-1

31.22 6.16 7.16 33.59 15.06 34.92 18.14

100 0 0 70 ± 4 7.3 ± 0.4 64 ± 3 22 ± 1

5.3 ± 0.3 17 ± 1 7.7 ± 0.3 9.1 ± 0.5 23 ± 3 10.3 ± 0.5 8.5 ± 0.3

5.3 0 0 6.4 1.7 6.6 1.9

Figure 3. 13C CP/MAS NMR spectra at a contact time of 2 ms. (a) Surface MT-4, (b) surface MT-1, (c) surface MD-4, and (d) surface MD-1.

monitored in a variable contact time experiment. The intensity is expected to vary with contact time t according to eq 2,15 and each signal was fit separately to eq 2 using nonlinear regression with three adjustable parameters: (1) the equilibrium intensity M0, (2) the time constant associated with cross-polarization, TCH, and (3) the 1H relaxation time in the rotating frame, T1ρ. M0 1−

TCH T1ρ

⎛ ⎛ ⎞ ⎛ ⎞⎞ ⎜exp⎜⎜ −t ⎟⎟ − exp⎜ −t ⎟⎟ ⎜ ⎝ TCH ⎠⎟⎠ ⎝ ⎝ T1ρ ⎠

± 0.3

± ± ± ±

0.5 0.3 0.5 0.3

density C1 (μmol/m2)

% trans

0 17 ± 1 7.7 ± 0.3 2.7 ± 0.5 21 ± 3 3.7 ± 0.5 6.6 ± 0.5

100 n/a n/a 100 48 ± 3 69 ± 4 51 ± 3

surfaces.12,14 To determine the percentage of long and short chains actually on the surface of each mixed-phase sample, the relative number of long chains was obtained by adding the equilibrium intensities of each of the three C18 peaks and dividing by 18 because there are 18 carbons that contribute to the intensities of these signals. To determine the number of short chains, the intensity of the CH3 peak was used; this intensity was divided by 1 or 2 for the trifunctional or difunctional chains, respectively, reflecting the number of carbons that contribute to this signal in each case. The relative number of long and short chains was used to obtain an average chain length and an average molar mass, and these average values were used in eq 1 to determine the ligand density on the surface, as has been done previously for mixed-phase samples.12 The percentage of long and short chains for each sample and the percentage carbon and the ligand density for each sample are summarized in Table 2. A comparison of the percentage of long chains in the reaction mixture to the percentage actually bonded to the surface reveals differences among the surfaces. When the percentage of long chains in the reaction mixture is high, the percentage of long chains on the surface exceeds that in the reaction mixture for both difunctional and trifunctional short chains. Although long chains comprise only 55% of the ligands in the reaction mixture for surfaces MT-4 and MD-4, 70% of the ligands attached to surface MT-4 and 64% of the ligands on MD-4 are long chains. This is surprising because the smaller short chains were expected to be more reactive than the bulkier long-chain ligands. By contrast, the percentage of long chains incorporated on the surface is the same or lower than expected when the reaction mixture contains a small percentage of long chains. The MT-1 surface contains only 7% long chains compared to 23% in the reaction mixture, and the percentage of long chains on surface MD-1 (22%) is the same as the percentage in the reaction mixture (24%). Further study on additional surfaces prepared using a wider range of long/shortchain ratios in the reaction mixture is necessary to explain these results in terms of the reactivities of individual ligands, and this will be examined in a future study. 13 C NMR also provides insights into the conformation of the long chains on the surface because separate signals are observed for trans and gauche chain conformations.11,27 Only one signal is observed for the interior carbons in the 13C spectrum of the single-phase C18 surface (SL), and the chemical shift of 34 ppm is indicative of all-trans bonds in the chain.6,7,13,17,18 By contrast, the 13C spectra of several of the mixed-phase surfaces contain two signals in this region, with the upfield signal at 31 ppm attributed to gauche defects in the long-chain conformations,11,13,17 indicative of an equilibrium mixture of trans and gauche conformations.28 Only one main peak at 34 ppm is observed in the spectrum of MT-4 with a small upfield shoulder, indicating that essentially all of the long chains exist

long- to short-chain ligands in the reaction mixture. For surfaces MT-4 and MD-4, a 4:1 volume ratio of long- to shortchain ligands was used, corresponding to a mole percentage of 55% long chains, and a 1:1 volume ratio was used for surfaces MT-1 (23% long chains) and MD-1 (24% long chains). The 13 C spectra of these mixed-phase surfaces contain signals from both ligands (Figure 3), and the intensity of these signals was

intensity(t ) =

density C18 (μmol/m2)

(2)

Once the equilibrium intensities were obtained, they were used for quantitative analysis, an approach that has been shown to be reliable with other single-phase and mixed-phase 4978

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in the trans conformation, with a small number of gauche defects. However, two distinct signals are observed in the spectrum of MD-4, indicative of a significant fraction of gauche bonds in the long chains. The relative intensity of these two signals can be used to estimate the number of ordered, all-trans conformations for the long chains on the mixed-phase surfaces (Table 2). Variable contact time 13C spectra data also enabled the measurement of the spin−lattice relaxation time in the rotating frame, T1ρ, for the ligand protons. The intensities of the signals corresponding to short chains, trans long chains, and gauche short chains were measured and fit separately to eq 2 to obtain T1ρ relaxation times for protons in each of these types of chains; the results are summarized in Table 3. Short-chain single-phase surfaces ST and SD are not included in Table 3 because these relaxation times are too long to be measured.

structures shown in Figure 5: −OSi(OH)2R, designated as T1, −O2Si(OH)R, designated as T2, and −O3SiR, designated as T3,

Table 3. Proton T1ρ Relaxation Times Obtained from Variable Contact Time 13C Data

Figure 5. Possible structures for (left) trifunctional ligands and (right) difunctional ligands.

sample

short-chain protons T1ρ (ms)

SL MT-4 MT-1 MD-4 MD-1

n/a 14 ± 2 120 ± 20 27 ± 5 >100

trans long-chain protons T1ρ (ms)

gauche long-chain protons T1ρ (ms)

± ± ± ± ±

n/a n/a 77 ± 8 33 ± 3 >100

11 15 21 17 22

1 1 1 1 1

respectively, where R is an alkyl chain.25 The chemical shifts for silicon atoms in these structures are the same regardless of the length of the alkyl chain R, and these signals are seen in the 29Si spectra of all derivatized surfaces (Figure 4b−h). The apparent difference in the signal-to-noise ratio in the spectra of ST (Figure 4c) and MT-1 (Figure 4f) surfaces is due to the extremely high density of ligands on these surfaces, resulting in an extremely large signal for T3 structures in these spectra. Silicon atoms with attached difunctional ligands resonate at a different chemical shift than silicons with trifunctional ligands,11,13,19,22,25 with a signal at −10 ppm observed for −OSi(OH)R2 structures, designated as D1, and a signal at −20 ppm observed for −O2SiR2 structures, designated as D2. No signals for D1 structures are observed in the 29Si spectra for the single-phase or mixed-phase surfaces containing difunctional ligands (Figure 4d,g,h). This indicates that there are no silanol groups attached to difunctional ligands; all difunctional ligands form two attachments, either to the surface or to another ligand. The relative intensities of different signals in a 13C CP/MAS spectrum of modified silica vary as the contact time is varied. Different carbons within the alkyl chain of the attached ligands have different mobilities. Carbons near the unbound end of the chain are more mobile than those near the surface,29 and the increase in mobility decreases the cross-polarization efficiency of carbons at the chain end. Previous work has shown that the time constant for cross-polarization, TCH, for individual carbons in the chain decreases as the distance from the surface increases.16,21,29 Therefore, quantitative analysis of 13C CP/ MAS spectra requires fitting intensities from variable contact time spectra to eq 2 to obtain equilibrium intensities, undistorted by differences in the cross-polarization efficiency. Different behavior is observed for relative intensities in a 29Si CP/MAS spectrum of modified silica. The intensities of Q2 and Q3 signals in unreacted silica exhibit a similar dependence on the contact time, with the maximum intensities in variable contact time spectra observed at approximately 5 and 7 ms, respectively.23 Ligand attachment does not significantly alter the response of these signals to cross-polarization, with similar values observed for the cross-polarization time constant, TSiH, with and without attached ligands.24 A similar dependence on contact time is also observed for silicons with attached ligands, where similar values for TSiH and the proton relaxation time in

29 Si NMR. The 29Si spectrum of unreacted silica gel (Figure 4a) contains three signals at chemical shifts of −90, −100, and

Figure 4. 29Si CP/MAS NMR spectra at a contact time of 5 ms. (a) Unreacted silica gel, (b) surface SL, (c) surface ST, (d) surface SD, (e) surface MT-4, (f) surface MT-1, (g) surface MD-4, and (h) surface MD-1.

−110 ppm, which have been assigned23 to silicon atoms with two attached hydroxyl groups, designated as Q2, silicons with one attached hydroxyl groups, designated as Q3, and silicons with no hydroxyls, designated as Q4, respectively. The attachment of trifunctional ligands leads to a similar triad of signals at −45, −60, and −70 ppm resulting from the 4979

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Table 4. Quantitative Results from 29Si CP/MAS Spectra Using a 5 ms Contact Time surface SL ST SD MT-4 MT-1 MD-4 MD-1

% T1 4.6 ± 3.7 ± n/a 3.3 ± 1.7 ± 1.6 ± 6.3 ±

0.5 0.4 0.3 0.2 0.2 0.6

% T2 46 ± 23 ± n/a 32 ± 18 ± 30 ± 43 ±

2 1 1 1 1 2

% T3 49 ± 73 ± n/a 65 ± 81 ± 68 ± 50 ±

2 3 3 3 3 2

% crosslinkinga 81 ± 90 ± n/a 87 ± 94 ± 89 ± 81 ±

3 3 3 3 3 3

density 29Si NMR (μmol/m2)b 5.3b 19 ± 2 4.6 ± 0.5 8.2 ± 0.8 27 ± 3 7.7 ± 0.8 5.6 ± 0.6

density %C (μmol/m2)c 5.3 17 7.7 9.1 23 10.3 8.5

± ± ± ± ± ± ±

0.3 1 0.3 0.5 3 0.5 0.3

unreacted silanols (μmol/m2)d 2.2 2.1 2.5 1.7 1.9 2.1 2.8

± ± ± ± ± ± ±

0.2 0.2 0.2 0.2 0.2 0.2 0.3

secondary silanols (μmol/m2)d 2.9 ± 5.1 ± none 3.5 ± 4.9 ± 2.3 ± 1.0 ±

0.3 0.5 0.3 0.5 0.2 0.1

a Only trifunctional ligands are included when calculating the percentages of T1, T2, and T3 structures. The percent cross-linking was calculated using eq 3. bDensity values were normalized to the value of 5.3 μmol/m2 obtained for a single-phase surface with trifunctional C18 ligands. cDensities from Table 1 obtained from % carbon and 13C NMR results. dDensity values were normalized to the ligand density determined from % carbon for each sample.

the rotating frame have been observed for T1, T2, and T3 structures.12,14,18,30 In addition, previous studies have shown that the variation in intensity as a function of contact time is similar for silicons corresponding to T, D, and Q3 structures, with maximum intensities occurring at approximately 2 ms, 3− 5 ms, and 8 ms respectively.19 Furthermore, a graph of intensity versus contact time typically exhibits a broad maximum, with only small variations (less than 10%) generally observed for contact times within 2 to 3 ms of the maximum.12,14,19,23 This is within the uncertainty of the peak intensities because the peaks are broad and partially overlapped. A contact time of 5 ms is a good compromise to ensure that all peaks have near maximal intensity, and previous studies on surface-polymerized singleand mixed-phase surfaces, similar to the ones in this study, showed no significant differences between relative intensities obtained from a single spectrum obtained with a contact time of 5 ms and equilibrium intensities obtained by fitting variable contact time data to eq 2.12 Agreement between single and variable contact time data was also seen in a study of mixedphase surfaces prepared from long- and short-chain aminecontaining ligands.14 Furthermore, the unique nature of the ligand mixtures used in this study enabled detailed comparisons of quantitative results obtained from 29Si NMR versus percent carbon and nitrogen determined from elemental analysis. Excellent agreement with elemental analysis was observed when the relative intensities from a spectrum obtained with a single contact time of 5 ms were used for the quantitation of different structures on the surface, and this study concluded using variable contact time data does not improve the accuracy of the quantitative results from 29Si NMR.14 Other studies have reached the conclusion that relative intensities from a spectrum obtained with a 5 ms contact time are quantitative, and spectra obtained at a single contact time have been used extensively for the quantitative analysis of the relative amounts of different structures on the silica surface.11,13,17,18,30−32 To verify that the relative intensities from a single 29Si CP/ MAS spectrum can be used reliably for the quantitative analysis of these surfaces, two checks of the quantitative results with other data were performed. First, the 29Si NMR spectra were used to determine the percentage of long and short chains on surfaces MD-4 and MD-1, and these percentages were compared to those obtained from 13C NMR. For these surfaces, the total intensity of the signals for T1, T2, and T3 structures is a measure of the number of trifunctional ligands, and the intensity of the signal for D2 structures measures the number of difunctional ligands on the surface. This enables the calculation of the percentage of long and short chains on the

surfaces containing difunctional short chains, and these percentages obtained from 29Si intensities can be compared to estimates obtained from 13C spectra. The percentage of long chains was calculated to be 68 ± 3 and 21 ± 1%, respectively, for surfaces MD-4 and MD-1 respectively. These results agree well with the long-chain percentages of 64 ± 3 and 22 ± 1% obtained for these surfaces from the percent carbon and 13C NMR data (Table 2). This agreement provides strong evidence that the peak intensities are not distorted by the effects of crosspolarization because the calculation of the percentage of long chains requires comparisons between signal intensities for silicons in D versus T structures. Because of the significant differences in these structures, the relative intensities of these signals are more likely to be distorted by differing effects of cross-polarization than are the relative signal intensities for more similar structures. The absence of any observable distortions when comparing D and T structures confirms the validity of using relative intensities within an 29Si NMR spectrum obtained at a single contact time for quantitative analysis. However, because this comparison could be made only for surfaces MD-4 and MD-1, a second test of the validity of using single-contact-time 29Si data for quantitative analysis was performed. The total ligand densities were determined from the 29Si spectra and compared to the densities determined from 13 C NMR and elemental analysis. The ligand density on the surface was measured by adding the intensities of all of the signals corresponding to silicon atoms with attached trifunctional and/or difunctional ligands and dividing this intensity by the mass of the silica in the sample (Table 4). The densities determined from 29Si spectra were normalized to a value of 5.3 μmol/m2 for the single-phase surface composed solely of long chains because, unlike the mixed-phase surfaces, the density of this surface can be obtained directly from the microanalysis results for percent carbon. For the surfaces containing only trifunctional ligands, good agreement is observed between the density obtained from 29Si NMR and densities calculated from the percent carbon and 13C NMR data. However, for the surfaces with difunctional ligands, the density calculated from 29 Si spectra is systematically lower than the density calculated from microanalysis and 13C NMR. This discrepancy may be caused by a difference in the cross-polarization efficiency of silicons on surfaces containing difunctional versus trifunctional ligands. However, if this is true, then all signals must be affected the same because the relative intensities within the spectra of MD-4 and MD-1 agree with 13C NMR results. A more likely source of the decreased intensity in spectra of surfaces with 4980

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silanols and silicons in Q3 structures have one unreacted silanol, the intensity of the Q2 peak was multiplied by 2 and added to the intensity of the Q3 peak to obtain the total number of unreacted silanols. This total was divided by the total intensity of peaks corresponding to silicons with attached ligands (D and T structures) and multiplied by the ligand density from 13C and the percent carbon data (Table 4) to determine the density of the silanols that remain unreacted, and the results are summarized in Table 4. This approach depends only on the relative intensities within individual 29Si spectra; it does not require comparisons of intensities between different spectra. Similarly, the density of secondary silanols, those created by incomplete cross-linking of the attached ligands, can also be determined from the 29Si NMR data. Each ligand in a T1 structure creates two silanols, whereas T2 or D1 structures result in one secondary silanol per ligand. Because no signals due to D1 structures were observed, the intensity of T1 and T2 signals can be used along with the ligand density and percentage of long chains (Table 2) to estimate the density of secondary silanols created during the surface reaction (Table 4). To get the density of secondary silanols, peak intensities in each spectrum were normalized to the total ligand density for that surface as described above.

difunctional ligands compared to spectra of surfaces with only trifunctional ligands is the method used to normalize the intensities for each spectrum to enable comparison with elemental analysis results. To convert the intensity of silicons with attached ligands into a ligand density for each surface, the mass of the attached ligands was calculated from the percent carbon data and subtracted from the sample mass to obtain the mass of the silica gel. There are many assumptions inherent in these calculations, and the correction for ligand mass is made somewhat differently for difunctional versus trifunctional ligands, as described in the Experimental Section. Indeed, if the 29Si NMR estimates for the density of samples SD, MD-4, and MD-1 are compared to each other instead of the density for the surface containing trifunctional ligands, then reasonably good agreement with carbon data is observed for the ligand density of these surfaces containing difunctional ligands. Regardless of the cause of the discrepancy when comparing surfaces MD-4 and MD-1 to surfaces with only trifunctional ligands, the good agreement among surfaces SL, ST, MT-4, and MT-1 indicates that there are no significant distortions in the spectral intensities for these surfaces caused by cross-polarization. These results, in combination with the good agreement between the percentage of long- and short-chain ligands determined from 13C and 29Si data, indicate that relative intensities within a 29Si CP/MAS spectrum obtained with a single contact time of 5 ms can be used for the quantitative analysis for these surfaces, in agreement with many other studies.11−14,17,18,30−32 29 Si spectra can be used to determine the degree of crosslinking between ligands on the different surfaces. The percentages of the three structures, T1, T2, and T3, can be determined from the integrated intensities of the signals at −45, −60, and −70 ppm, respectively. The relative amount of these structures can be used to determine the extent of crosslinking,17 according to eq 3, and the results are summarized in Table 4. %cross‐linking =

1 2 (%T1) + (%T2) + %T3 3 3

■

DISCUSSION Ligand Density and Cross-Linking. The surface polymerization method used to create the mixed-phase surfaces is expected to result in the formation of a self-assembled monolayer, where ligands are cross-linked horizontally across the surface. Figure 6 depicts an artistic rendering of an idealized

(3)

The surfaces containing mixed trifunctional long and short chains (MT-4 and MT-1) are more extensively cross-linked than the single-phase C18 surface, as was observed previously with mixed-phase surfaces prepared using trifunctional ligands.5,12 For the mixed-phase surfaces containing difunctional ligands MD-4 and MD-1, the cross-linking of the long and short chains can be examined separately because silicon atoms with attached difunctional ligands have different chemical shifts compared to silicons with attached trifunctional ligands. The percent crosslinking listed in Table 2 is for trifunctional ligands only, which are exclusively long chains for these mixed-phase surfaces. The absence of a signal at −10 ppm for D1 structures indicates that the short chains are essentially 100% cross-linked in both samples containing difunctional ligands. By contrast, the crosslinking for the long chains is less than 90%, indicating a greater tendency for short chains to form cross-links compared to long chains even though the short chains are difunctional and the long chains are trifunctional. These results suggest that the length of the chain is more important than the functionality for the determination of the degree of cross-linking. The density of unreacted silanols could also be determined from the intensities of the Q2 and Q3 signals in the 29Si spectra. Because silicon atoms in Q2structures have two unreacted

Figure 6. Idealized mixed-phase surface composed of trifunctional long and (left) trifunctional and (right) difunctional short chains. Silicon, oxygen, carbon, and hydrogen atoms are represented by yellow, red, black, and blue spheres, respectively. For difunctional short chains, the third linkage for the long chains has been omitted for clarity. These chains would also cross-link in the second dimension to achieve complete cross-linking; only 1D cross-linking is shown.

horizontally polymerized mixed-phase surface formed when (a) both the long- and short-chain ligands are trifunctional and (b) the long chains are trifunctional but the short chains are difunctional. For simplicity and clarity, cross-linking is shown in only one dimension, but the chains can cross-link in both dimensions across the silica surface. In this idealized model, the small chains fit between the long chains, and all ligands are completely cross-linked, with one Si−O bond formed from the ligand to the silica surface and either two (trifunctional ligands) or one (difunctional ligand) Si−O bonds to adjacent ligands. Ideally, no silanols remain exposed on the surface because the original unreacted silanols are covered up by the cross-linked network of ligands whereas complete cross-linking prevents the creation of any new silanols. However, the actual surfaces prepared differ from this idealized model in several important 4981

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with mixed-phase surfaces prepared previously via surface polymerization,4,5,12 was expected to prevent vertical polymerization by restricting the availability of water to the silica surface. It is difficult to pinpoint the exact amount of surface water achieved by humidification, but water adsorption studies on other silica surfaces indicate that the water layer at the surface likely has a thickness of one to three water molecules (one to three monolayers of water). Earlier studies of water adsorbed to quartz plates indicate that 50% humidity corresponds to a monolayer of water on the surface, with multiple layers forming only when the humidity levels approached 90%.33 A later study of water adsorbed on glass indicates that 50% humidity corresponds to two to three monolayers,34 whereas adsorption isotherms generated on SiO2 powder indicate that 50% humidity represents approximately 1.5 monolayers of water.35 Although there may be more than one layer of water on the surface of these mixed-phase samples, the water is unlikely to migrate from the surface because the adsorption of water to water is even more energetically favored than the adsorption of water to silica.36 The larger size of the ligand molecules relative to water in combination with the close association of water with the silica surface should force all reactions to occur at the silica surface, preventing vertical polymerization. Nonetheless, vertical polymerization apparently has occurred, both for single-phase surface ST and mixed-phase surface MT-1. Mixed-phase surface MT-1 has an extremely high short-chain density, which is the cause of the unusually high overall ligand density well in excess of a monolayer. Furthermore, the percentage of long chains on the surface of MT-1 (7%) is much lower than the 23% of long chains in the reaction mixture. This is noteworthy because the other mixedphase surfaces have a long-chain percentage that is either the same as the percentage in the reaction mixture (MD-1) or slightly higher (MT-4 and MD-4). This increased concentration of short chains on MT-1 implies that the short chains are combining with each other to form short oligomers extending away from the surface. There is no indication of similar behavior for the other mixed-phase surfaces nor was vertical polymerization observed in mixed-phase surfaces prepared from a mixture of trifunctional C18 long chains and C3 short chains.12 It is possible that the water content necessary to achieve horizontal polymerization without allowing vertical polymerization may depend on the size and/or reactivity of the ligand. The trifunctional C1 short chains are the smallest of the ligands, so it may be easier for these ligands to react away from the surface, especially if more than a monolayer of water is present. Interestingly, the amount of cross-linking is greater for surface MT-1, containing vertically polymerized short chains, than for surface MT-4, which is horizontally polymerized. This suggests that the oligomers of short chains that attach to the surface also branch out horizontally to form more than one layer of cross-linked short chains on the surface. If this were not the case, then the number of ligands with one or more secondary silanols attached (T1 and T2 structures) would be much greater than is observed. Further insights can be gained by an examination of the degree of cross-linking for surfaces containing difunctional versus trifunctional short chains. For surfaces MD-4 and MD-1, the cross-linking for the long chains is measured separately from that for the short chains, whereas only the overall crosslinking, for both long and short chains, can be measured for MT-4 and MT-1, which complicates comparisons between the two types of surfaces. However, surface MD-4 has 89% cross-

ways. All actual mixed-phase surfaces contain both unreacted silanols remaining on the original surface and secondary silanols formed during the chemical modification process because the cross-linking is less than 100%. These secondary silanols represent defects compared to the theoretically perfect horizontally polymerized surface shown in Figure 6, which contains no secondary silanols, and these silanols will be discussed further in a later section. The distribution of long and short chains on the surface also differs from that of the idealized model because the percentage of long chains on the surface is greater than 50% for MT-4 and MD-4 but less than 50% for MT-1 and MD-1. Consequently, there must be either adjacent long or short chains on the surface, in contrast to the strict alternation of long and short chains depicted in Figure 6. One goal of using a mixture of long- and short-chain ligands instead of a single ligand is to increase the ligand density compared to that of a single-phase surface composed entirely of long chains, and all mixed-phase surfaces have a higher ligand density than surface SL, as seen previously.4,5,12 However, the increase in ligand density achieved by the incorporation of a small number of short chains is not just due to additional short chains filling in the spaces between the long chains. The percentage of short chains effects the density of long chains; the density of long chains on surfaces MT-4 and MD-4 is also greater compared to that on surface SL (Table 2). This increase in the long-chain density as well as the total ligand density suggests that the presence of short chains makes it easier for the bulkier long chains to react at the surface for both trifunctional and difunctional short-chain ligands. Short chains provide less steric hindrance, enabling more long chains to bond with the surface. The long-chain densities are nearly identical on surfaces MT4 and MD-4. However, surface MD-4 has a slightly higher density of short chains compared to surface MT-4, resulting in a slightly higher overall ligand density. Although there are two interfering chains instead of one when the short chain is difunctional, the angle that the two chains make with the surface is different than the angle associated with a single chain, which minimizes contacts with adjacent chains. Hence, difunctional short chains may be able to pack more closely with long chains than trifunctional short chains, especially when the number of short chains is small. When the percentage of difunctional short chains is increased (surface MD-1), the total density is lower than for surface MD-4. This lower ligand density for MD-1, in conjunction with the nearly identical longchain densities observed for surfaces MT-4 and MD-4, suggests that there may be an optimum ratio of long and short chains that results in maximum surface coverage. Dramatically different behavior is observed for surface MT-1 compared to that for MD-1. Although the overall ligand density of the other mixed-phase surfaces is consistent with monolayer coverage, the extremely high ligand density observed for MT-1 greatly exceeds that possible for a monolayer, and the singlephase surface composed exclusively of short chains (ST) shows similar behavior. This high coverage indicates that a significant amount of vertical polymerization has occurred, where ligands attach to other ligands to form chains that extend up from the surface, unlike the ideal case (Figure 6) where only horizontal polymerization across the surface occurs. Vertical polymerization is unexpected because the water content was carefully controlled by humidifying the silica gel to 50% relative humidity before allowing the ligands to react with the surface. A humidity level of 50%, chosen to enable direct comparison 4982

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Comparison of the number of trans conformers on the mixedphase surfaces provides insights into the factors that determine the conformation allowed for the long chains. The 13C spectra of both of the mixed-phase surfaces prepared using a 1:1 ratio of long to short chains in the reaction mixture (MT-1 and MD1) contain two peaks of nearly equal intensity at 34 and 31 ppm, indicating that only half of the chains are in an ordered, trans conformation. Despite the overall high coverage of these mixed-phase surfaces, especially the surface made using trifunctional short-chain ligands, both surfaces have essentially the same low density of long chains, leading to the same percentage of ordered trans conformations. This suggests that it is the density of long chains that likely dictates the number of gauche defects that can form. Whereas steric crowding caused by adjacent long chains forces these chains to be in a trans conformation, adjacent short chains, which are close to the surface, do not impede the movement of the long chains and allow more gauche conformations, resulting in bent long chains. These observations are consistent with the results obtained on single-phase surfaces. When the density of long chains is increased on the mixedphase surfaces, the percentage of trans long chains increases as expected, regardless of the functionality of the short chains. However, a distinct difference in the conformation of long chains is observed for the two surfaces containing a high percentage of long chains, MT-4 and MD-4. The density of long chains is essentially the same in both cases, but there are significantly more trans conformers for the surface containing trifunctional short chains. Essentially all of the long chains on surface MT-4 adopt trans conformations, as is observed for the single-phase surface SL. However, the use of difunctional short chains results in a significant number of gauche defects for long chains on surface MD-4. This indicates that the percentage of trans conformers depends on more than just the long-chain density on the surface. The difference in geometry for difunctional versus trifunctional ligands could account for the difference in the percentage of long chains in a trans conformation. When both the long and short chains arise from trifunctional ligands, both the long and short chains are aligned, forcing the long chains into trans conformations when the density of long chains is high. Short chains from difunctional ligands are not aligned the same way, so more gauche defects are allowed. It is also possible that differences in the percentage of trans conformers are caused by a difference in the degree of clustering of long chains on the surface. However, differences in the clustering of long chains would affect the mobility of the chains, and no significant difference is observed in the long-chain mobility, as discussed in the next section. Other workers have used different synthesis methods to prepare surfaces with short-chain ligand “spacers” between long-chain ligands, and it is interesting to compare results from previous studies to those presented here. Kühnle and coworkers have examined the surface formed when chemical modification is done in two stages: (1) the reaction of shortchain, monofunctional ligands and (2) surface or solution polymerization using trifunctional long chains.39 As observed for the mixed-phase surfaces in this study, the chain conformation was shown to depend on the surface coverage of C18 chains, with the trans conformation favored by the high coverage of long chains (greater than 3 μmol/m2) and gauche conformations predominant at low coverage.39 However, the bonded phases prepared by Kühnle and co-workers using surface polymerization showed less cross-linking among the

linking for trifunctional long chains and 100% cross-linking for difunctional short chains compared to 87% combined crosslinking for trifunctional long and short chains for surface MT-4, indicating that a greater number of the possible ligand sites have reacted, either with the surface or another ligand, on surface MD-4. This is consistent with closer packing between long and short chains on surface MD-4 but does not necessarily mean that there are more bonds between adjacent ligands on this surface. Because each difunctional ligand has only two possible reaction sites, it is likely that there are fewer connections between ligands on surface MD-4 compared to the number on surface MT-4. Increasing the number of short chains has a different effect on the degree of cross-linking when the short chains are difunctional versus trifunctional. For mixed-phase surfaces containing trifunctional ligands, the degree of cross-linking increases as the percentage of short chains increases, reflecting the greater tendency of short chains to form cross-links. However, the opposite trend is observed for the surfaces prepared using a mixture of trifunctional and difunctional ligands. For these samples, more cross-linking is observed for the trifunctional long chains when the percentage of short chains is decreased, with surface MD-4 exhibiting more crosslinking than surface MD-1. There are two factors that could account for these observations. It is easier to form a 2D network of cross-linked ligands when trifunctional ligands are used, and because only the long chains are trifunctional, surfaces with a greater number of long chains have more trifunctional ligands, resulting in more cross-linking. Second, because short chains cross-link more efficiently than long chains, increasing the number of long chains increases the probability that the short chains will cross-link with long chains rather than with other short chains. This would result in a greater percentage of long chains involved in cross-linking when the ratio of long/short chains on the surface is increased. Conformation of Long Chains. Previous studies on single-phase polymeric surfaces composed of C22 chains showed that the number of all-trans conformations varied with the density of chains on the surface for both difunctional and trifunctional ligands.13 For difunctional ligands, a single peak at 30 ppm attributed to gauche defects was observed in the 13C NMR spectrum at a low coverage of 3.6 μmol/m2, indicative of an equilibrium mixture of trans and gauche conformations for all chains.28 As the density of chains was increased, the amount of all-trans conformations increased. Similarly, increasing the density of trifunctional C22 ligands resulted in fewer gauche defects, with exclusively trans conformations observed as the coverage approached that expected for a monolayer.13 These trends were confirmed by molecular dynamics calculations on polymeric surfaces composed of both difunctional and trifunctional C 18 ligands.37,38 Similar results were obtained on single-phase surfaces prepared using trifunctional C30 ligands. At a low coverage of 1.1 μmol/m2, the 13C spectrum contained only one peak corresponding to trans/gauche conformations, but a second peak due to trans conformers was observed as the chain density increased,18 with the majority of chains in an all-trans conformation at a density of 4.1 μmol/m2. Our results for the single-phase surface composed of trifunctional C18 ligands are consistent with these observations because the coverage of long chains on surface SL is expected to be sufficiently high (5.3 μmol/m2) to force essentially all the chains into an ordered trans conformation, as was observed. 4983

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than that observed for the crystalline component (all trans), indicating that chains in trans conformations of polyethylene are more rigid.27 The observation of longer 1H T1ρ relaxation times for the more mobile chains attached to the surface is also consistent with previous studies on chemically modified silica surfaces, where longer relaxation times have been attributed to the increased mobility of attached ligands.6,11,12,20,21 For surface MT-4, the relaxation time of the short-chain protons is the same as for the long-chain protons. The observation of a single relaxation time is indicative of rapid spin diffusion associated with more rigid molecules,15 and the short relaxation time for both long- and short-chain protons indicates that the mobility of all surface ligands is restricted. This restricted mobility, in combination with the high total chain density, suggests that this surface consists of a densely packed, highly ordered array of both long and short chains. The tight packing and high degree of order is consistent with the observation that essentially all of the long chains adopt a trans conformation, with very few gauche defects present. By contrast, short chains and both types of long chains on surface MT-1 all have different relaxation times, and all are longer than those for surface MT-4. This indicates that ligands on surface MT-1 are more mobile than on surface MT-4 despite the extremely high chain density on MT-1. Although the overall ligand density is high, there is a lower density of long chains on MT-1, so there are fewer of the bulky chains that are likely to hinder the motion of the ligands. The notion that the density of long chains, not the overall ligand density, determines the ligand mobility is supported by comparing surfaces MT-1 and MD-1 to MT-4 and MD-4. The density of long chains is nearly identical for MT-1 and MD-1 but significantly lower than for MT-4 or MD-4. The T1ρ relaxation times for trans long chains on surfaces MT-1 and MD-1 are the same but somewhat longer than the relaxation times for surfaces MT-4 and MD-4, indicating that a lower density of long chains leads to increased chain mobility. These results are consistent with molecular dynamics simulations that show that the chain order increases as the ligand density increases.38 Deviation from this tendency of increased mobility at lower long-chain density is seen when the mixed-phase surfaces are compared to single-phase surface SL. Although surface SL has a lower chain density than surfaces MT-4 and MD-4, the proton relaxation times measured for long chains in trans conformations on surfaces MT-4 and MD-4 are slightly longer than for surface SL, indicating that the long chains on the mixed-phase surfaces are somewhat more mobile than on the single-phase surface. The formation of clusters of long chains on the surface would decrease the mobility of the chains because of steric hindrance. Because there are more long chains on the mixedphase surface than on the single-phase surfaces, this increase in mobility for long chains on mixed-phase surfaces suggests that the chains are more spread out than on the single-phase surface, where clusters of long chains are more likely to occur. This is consistent with the expectation that short chains will fit in the spaces between the long chains, thereby spreading out the long chains compared to single-phase surface SL. The long-chain relaxation times are essentially the same for surfaces MT-4 and MD-4, which have the same long-chain density, suggesting that there are no significant differences in the degree of clustering of long chains when trifunctional versus difunctional ligands are used. There are distinct differences in the two surfaces, however. Although the behavior of the long

long chains for the same total coverage as the number of shortchain spacers is increased.39 Because only the long chains are capable of forming cross-links on this bonded phase, the decrease in long-chain cross-linking as the density of short chains is increased indicates that the short chains serve to spread out the long chains and prevent the formation of clusters of large chains, consistent with the results in the current study of mixed-phase surfaces. Chain Mobility. An examination of the relaxation times of the ligands, in conjunction with the surface densities of long and short chains, provides insights into the morphology of the mixed phase formed on the surface of the silica. The magnitude of the relaxation time in the rotating frame, T1ρ, is a complex function of all of the molecular motion occurring in the sample, so the interpretation of relaxation times in terms of molecular mobility must be done with caution. Proton T1ρ values can be measured indirectly by fitting 29Si or 13C intensities obtained from variable contact time CP/MAS experiments to eq 2. These relaxation times are primarily determined by the molecular motion of the protons that are transferring polarization to the heteronucleus in the cross-polarization experiment. 1H T1ρ values obtained from 29Si variable contact time data can be difficult to interpret because both ligand protons and surface silanols can contribute to the crosspolarization of silicon nuclei, so the relaxation times reflect the motion of both the substrate and the ligand. The interpretation of proton T1ρ values obtained from 13C NMR is much more straightforward because the cross-polarization of protonated carbons arises almost exclusively from the directly attached protons. Proton T1ρ relaxation times are probes of molecular motion in the kilohertz regime, with the most efficient relaxation (shortest relaxation times) corresponding to motion near the frequency of the spin-lock field.15 Molecular motion is typically characterized by an effective correlation time, τc, which is inversely proportional to the frequency of motion. The proton T1ρ relaxation time is at a minimum when τc−1 corresponds to the frequency of the spin-lock field; whether the relaxation time increases or decreases with increasing mobility depends on whether the motion causing the relaxation is faster or slower than the spin-lock frequency, in this case 55 kHz. Previous measurements of 13C T1 relaxation times and the 13C−1H nuclear Overhauser effect (NOE) for C18 chains attached to silica indicate that the ligand motion is near the motional narrowing limit, with a rate of reorientation of the silane groups near 50 MHz.16,29 A reorientation rate near 50 MHz would mean that the motion of the alkyl chains is much faster than the spin-lock frequency of 55 kHz used in the CP/MAS experiments. In this case, a faster motion of the attached ligands would increase the proton T1ρ relaxation time,16,29 and this is consistent with the observation of longer relaxation times for long chains in gauche conformations compared to trans conformations, for all surfaces where gauche chains were observed (Table 3). Long chains in trans conformations are expected to be more rigid than those in gauche conformations, and this mobility difference has been observed previously,for both long chains attached to silica and in polyethylene. Twodimensional wide-line separation (2D WISE) experiments on attached chains have shown that the trans chains have shorter T2 relaxation times, indicative of slower motion6,13,40 Furthermore, the 13C T1 relaxation time of 175 ms observed for the noncrystalline component of polyethylene (trans/ gauche equilibrium of chain conformations) is much shorter 4984

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on the surface compared to trifunctional ligands. Surface MD-4, which incorporates a low percentage of difunctional short chains, shows a slight increase in unreacted silanols compared to surface MT-4, which incorporates the trifunctional short chains at the same percentage as for MD-4. A more substantial increase is observed for surface MD-1, which has a higher percentage of difunctional ligands compared to surface MD-4, confirming the expectation that difunctional ligands tend to form fewer bonds with the surface than trifunctional ligands. In addition to silanols originally on the surface of the silica substrate, secondary silanols, on silicon atoms from attached ligands, are created during the chemical modification of the surface as a result of the incomplete cross-linking of the ligands. There are fewer secondary silanols on surface MD-4 than on MT-4 and fewer still on surface MD-1. This is expected because the difunctional ligands on these surfaces are completely crosslinked, so secondary silanols arise from the incomplete crosslinking of the trifunctional ligand. Interestingly, the surface with the highest overall percentage of cross-linking among trifunctional ligands is MT-1, which also has the highest density of secondary silanols. This apparent contradiction is caused by the vertical polymerization of the short chains, which creates a larger number of secondary silanols than would be created during the formation of a highly cross-linked, horizontally polymerized mixed-phase surface.

chains is the same, the longer relaxation time for the short chains on MD-4 suggests that the mobility of the short chains is greater for MD-4 than for MT-4, despite similar densities of both long and short chains for these two surfaces. The difunctional ligands have fewer bonding sites available, so there are likely to be fewer points of attachment to other ligands. This would enable the increased short-chain mobility observed for MD-4 compared to that for MT-4. Unreacted Silanols. Ligands attach to the surface by reacting with silanols on the silica substrate, so the number of silanols originally present that remain unreacted is an indirect measure of the number of ligands that have formed a bond with the surface. Whether these unreacted silanols are exposed or covered by ligands, they will give rise to signals at −100 ppm for Q3 structures corresponding to silicon atoms with a single attached silanol and −90 ppm for Q2 structures corresponding to geminal silanols on a single silicon atom. However, the interpretation of the intensity of the signal corresponding to Q3 structures is complicated by the fact that silica gel inevitably contains defects resulting in the formation of internal silanols, which also resonate at −100 ppm. Deuterium exchange experiments suggest that these internal silanols likely account for less than 10% of the intensity of this signal.41 Nonetheless, the density of unreacted silanols measured by NMR provides an upper limit to the number of silanols remaining on the modified surfaces because the NMR estimate includes both internal and surface silanols. Unfortunately, differences in the efficiency of cross-polarization in the unreacted silica gel versus silica with attached ligands reduce the intensity of signals in a 29Si CP/MAS spectrum compared to the signal intensity after ligand attachment, and this precludes a direct comparison of the density of unreacted silanols before and after the attachment of ligands to the surface.14 The density of unreacted silanols on the surface of the silica gel used to make the modified surfaces in this study is not known. However, the density of unreacted silanols was determined to be 8.5 μmol/m2 on the surface of fume silica with a surface area of approximately 200 m2/g.31 If this estimate of the number of surface silanols is assumed to be valid for the silica in this study, then the density of unreacted silanols remaining on the surface of the modified silica (Table 4) can be subtracted from 8.5 μmol/m2 to obtain a lower limit for the silanol sites that reacted during the chemical modification of the surface. For surface MT-4, this yields a difference of approximately 7 μmol/m2 compared to a ligand density of 9 μmol/m2. Although there are many assumptions inherent in these calculations, these ballpark estimates suggest that a vast majority of ligands on surface MT-4 are bonded to the surface, not just connected to each other. However, for surface MT-1, the ratio of ligands attached to reacted silanols is much higher than for MT-4, indicating that many of the ligands are not actually bonded to the surface but are attached to each other. This is consistent with vertical polymerization on surface MT-1. Single-phase surface SL has a somewhat higher density of unreacted silanols but a lower ligand density compared to the mixed-phase surfaces. This indicates that a higher percentage of ligands are bonded to the single-phase surface than to the mixed-phase surfaces. These results suggest that, compared to long chains, short-chain ligands are more likely to attach to each other without bonding to the surface, thereby covering up unreacted surface silanols. Difunctional ligands can form only two bonds, to the surface and/or adjacent ligands, so difunctional ligands are likely to leave more unreacted silanols

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CONCLUSIONS The structural morphology and mobility resulting from the surface polymerization of a mixture of long (C18 chains) and short (C1 chains) ligands have been characterized by solid-state NMR. Mixed-phase surfaces prepared using either trifunctional or difunctional short-chain ligands have a higher overall density and greater cross-linking compared to the surface polymerization of exclusively long-chain ligands, indicating that short chains fill in the spaces between the long chains and promote cross-linking with neighboring chains by reducing crowdedness and steric hindrance on the surface. It appears that some optimum cross-linking is achievable by incorporating an appropriate number of short-chain spacer molecules. Rough estimates of silanol densities suggest that a majority of ligands form at least one bond with the silica surface. When the reaction mixture contains a 4:1 ratio of long to short chains, there is a greater density of long chains on the mixed-phase surface than obtained when long chains are used exclusively to form a single-phase surface, regardless of whether the short chains arise from difunctional or trifunctional ligands. This indicates that the short chains facilitate not just a greater overall density but also a greater density of long chains. However, there are distinct differences in the mixed-phase surfaces created using trifunctional versus difunctional short chains. Despite the similar density of long chains on the two surfaces, difunctional short chains result in a more loosely connected network that is more mobile and contains a greater number of gauche defects compared to trifunctional ligands. This is caused primarily by the difference in chain packing for difunctional short chains containing two methyl groups and trifunctional chains with only one methyl group, along with the reduced ability of difunctional chains to cross-link to other ligands. When the percentage of short chains in the reaction mixture is increased, the same density of long chains is obtained on the surface regardless of whether the short chains are trifunctional or difunctional. However, a significant amount of vertical 4985

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polymerization occurs when the short chains are trifunctional, but this does not occur when difunctional short chains are used to form a mixed-phase surface. It is possible that vertical polymerization is induced by the presence of more than one layer of water on the surface. The actual reaction and crosslinking process is spontaneous and is effectuated quickly, likely within the first 30 min of the reaction. Excess water vapor on the substrate surface, beyond that needed for surface polymerization of the ligands, could potentially create room for the further reaction of ligands away from the surface. This would result in molecular stacking, where ligands line up on top of each other, causing the formation of oligomers extending up vertically from the surface. This explanation, although speculative, is consistent with the observation that vertical polymerization occurs only when trifunctional short chains are used. The possibility of stacking caused by excess water is expected to be more pronounced with trifunctional short chains that are able to fit easily in the crevices in search of any excess water on the substrate surface. The difunctional short chains are bulkier, so they would not be expected to exhibit the same tendency for vertical polymerization as trifunctional short chains for the same amount of available water on the surface. The hypothesis that excess water is responsible for the vertical polymerization of short-chain ligands can be tested by reducing the water content on the surface through lower humidity levels, and this will be the focus of a future investigation. Regardless of the cause, the vertical polymerization of short chains seen for mixed-phase surface MT-1 does not preclude the eventual cross-linking needed to seal the surface.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to the State University of New York College of Environmental Science and Forestry (SUNY-ESF) for the use of their 300 MHz NMR for these studies. We also are grateful to Dr. David Kiemle, Director of Analytical and Technical Services at SUNY-ESF, for his assistance with the NMR experiments. We are grateful for funding for this project from the Scholarly and Creative Activities committee at Oswego State University.

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