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J. Phys. Chem. B 2007, 111, 10208-10216
Adsorption of Acridine Orange at a C8,18/Water/Acetonitrile Interface Antony Fouqueau and Markus Meuwly* Department of Chemistry, UniVersity of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland
Raymond J. Bemish Pfizer, Inc., MS-118A-2003, Eastern Point Road, Groton, Connecticut 06378 ReceiVed: March 2, 2007; In Final Form: June 25, 2007
Fully atomistic simulations are used to characterize the molecular dynamics (MD) of acridine orange (3,6-dimethylaminoacridine) at a chromatographic interface. Multiple 1 ns MD simulations were performed for acridine orange at the interface between three different acetonitrile/water mixtures (0/100, 20/80, and 50/50) with C8 and C18 alkyl chains. The diffusion coefficient, D, of acridine orange in pure solvent was found to be 4 times smaller at the water/C18 interface (D ) 0.022 × 10-4 cm2/s) than in bulk water (D ) 0.087 × 10-4 cm2/s), in qualitative agreement with experiment. Rotational reorientation times were 20 and 700 ps, which also agree favorably with the measured time scales of 130 and 740 ps. Contrary to experiment, the simulations found that for increasing surface coverage, the diffusion coefficient for acridine decreased. Detailed analysis of the solvent structure showed that the transport properties of acridine were primarily governed by the solvent distribution above the functionalized surface. The solvent structure, in turn, was largely determined by the surface consisting of the silica layer, the alkyl chains, and their functionalization.
I. Introduction The modifications of the interactions of analyte and solvent molecules within a solvent at the boundary of or in contact with a derivatized surface forms the fundamental principle behind chromatographic reversed-phase HPLC separations. The delicate balance between the interactions of the many components in the system fundamentally controls the retention of a compound on an HPLC stationary phase and, ultimately, its separation from structurally similar compounds. As simple as the system appears to be, the nature of the interactions has been difficult to explore directly. Computationally, the system also presents challenges. Unlike large proteins, which are constrained to move about a backbone, these systems consist of many solvent molecules that explicitly interact with the analyte molecules as well as the derivatized surface. Therefore, few simplifications can be made. In the system relevant for HPLC, there are three interacting components: the analyte molecule, the solvent, and the alkylchain-derivatized silica surface. The solvent system commonly used in HPLC is composed of water (H2O) and acetonitrile (CH3CN). The ratio of these is adjusted to change the hydrophobic character of the solution and affect the elution of analyte molecules. Not only does acetonitrile play a role in solvent polarity change, but the hydrophobic methyl group connected to a hydrophilic cyano group also acts as an extremely small surfactant. The literature contains abundant spectroscopic information (IR,1-5 Raman,6,7 UV-vis,8,9 NMR10-15) about acetonitrile/water mixtures, although the general nature of the intermolecular interactions is not yet fully understood. In the study of mixtures of water with other liquids, Naberukhin and Rogov16 investigated the effect of the additional component on the water structure. The formation of regions with enhanced water structure surrounded by a more disordered mixture of water and solute was referred to as “microheterogeneity”. Later, on the basis of excess volumes, viscosity, and the dielectric
constant, Moreau and Douhe´ret17 postulated that there are three regions in the entire composition range of water-acetonitrile where the solution is thought to separate into regions of acetonitrile and regions of water. For molar fractions of acetonitrile xACN < 0.2, the acetonitrile molecule occupies the cavities between the water molecules without enhancing the water structure; for 0.2 e xACN e 0.8, microheterogeneous behavior occurs with large aggregates formed; and for xACN > 0.8, the acetonitrile structure is disrupted by water. These observations have led to the concept of microheterogeneity18-20 in which the solution is considered to separate into ACN-rich regions and water-rich regions. Recently, Reimers and Hall21 proposed that microheterogeneity is not switched on and off at discrete concentrations. Instead, their experimental Raman spectra indicate that the system undergoes a continuous transition over the entire solvent composition with the changes simply being that each component has solvent clusters that grow or shrink with respect to each other, depending on the solution composition. The interactions of the derivatized silica with the analyte molecule and the solvent are equally complex. The alkyl chain is very nonpolar, whereas the surface to which it is attached is easily ionized. This is moderated experimentally by endcapping reactive groups or changing the nature of the alkyl chain.22 The common alkyl chain density found in commercially available HPLC columns should provide significant steric hindrance to intercalation by bulky analyte molecules. However, experimentally, longer chains show stronger hydrophobic interactions, implying more than the ends of the chains is involved in the interactions.23 In this paper, we describe the application of molecular dynamics simulation techniques to investigate the transport of acridine orange in a C8 and C18 alkylsilane chromatographic model in order to understand the specific mechanism of retention process that has been observed with C8 and C18 stationary
10.1021/jp071721o CCC: $37.00 © 2007 American Chemical Society Published on Web 08/09/2007
Acridine Orange Adsorption at C8,18/H2O/CH3CN
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10209 TABLE 1: Ligand Density (in µmol/m2) for the Two Different Coverages Studieda ligand low load high load
-(CH 2)x -CH 3
-OH
-CH 3
0.88 (8) 2.65 (24)
3.10 (28) 2.21 (20)
3.10 (28) 2.21 (20)
a Numbers in parentheses correspond to the number of ligands on a surface of 64 possible locations. x ) 8, 18
Figure 2. Definition of the atoms used for the estimation of the reorientation of acridine. b x ) N1C B7 X C4C B9, b y ) C4C B9, and b z ) N1C B7.
Figure 1. Side view (y-z plane) of the starting structure after solvation. Silicon, oxygen, carbon, nitrogen, and hydrogen atoms are in yellow, red, light blue, dark blue, and white, respectively. Water and acetonitrile are represented with thin sticks. C8 alkyl chains are represented with thick sticks.
phases. We have simulated C8 and C18 stationary phases with acridine orange over a range of different initial positions (440 Å from bulk silica) to investigate acridine transport at a chromatographic interface. Structural features, such as end-toend chain length, solvent density, charge state of analyte, and position of acridine orange, are analyzed in detail. The present work is structured as follows. In the next section, the theoretical and computational methods are discussed. Next, the solvent density distributions and acridine transport are presented. Finally, the results are compared between the simulations and experiments and discussed in the concluding section. II. Computational Methods A. Description of the Chromatographic Column. A model silica support was constructed by slicing two 8.75-Å-thick segments of the (101) face of a quartz crystalline lattice with width dimensions of 36 × 41 Å. This resulted in two surfaces with a vicinal silanol density of 3.1 µmol/m2. Chromatography models were created by covalently tethering alkylsilane ligands (with the alkyl chains in an initial all-trans conformation) to the silanol oxygen atoms of the quartz surface and at a position orthogonal to the bulk quartz (Figure 1). A 80-Å-thick solvent box (acetonitrile/water mixture) was added between the two surfaces, resulting in a unit cell with dimensions of 36 × 41 × 97 Å. Alkyl chains were evenly distributed over the surface silanols in a randomized fashion to result in a specific surface coverage (cf. Table 1). Depending on the solvent mixture, the systems with 0.2 and 0.5 volumic fraction of acetonitrile contain 10 962 and 12 171 atoms, respectively. For the present work, the transferable intermolecular potential three-point (TIP3P)24 water model was used. For the acetonitrile
(ACN) molecule, all hydrogen atoms were assigned to the existing aliphatic hydrogen (atom type HA), the methyl-C atom was assigned to the aliphatic SP3 carbon (CT3), the cyano-C was assigned to polar carbon (C), and the nitrogen atom was assigned to the proline nitrogen (N).25 The CN equilibrium bond length from proline (1.30 Å) was modified to 1.16 Å, which is compatible with the experimental structure determined by gasphase microwave and infrared spectroscopy.26 With these parameters, the root-mean-square distance (rmsd) between the optimized structure and the experimental structure26 is better than 0.05 Å. For acridine orange (Figure 2), all hydrogen atoms attached to carbon atoms were assigned to aromatic hydrogen (HP), hydrogens attached to nitrogen atoms were assigned to N-terminal (HC), all C atoms were assigned to the aromatic carbon (CA), and the nitrogen atoms were assigned to amide nitrogen (NH2). The partial atomic charges of the alkyl chains and acetonitrile molecule were obtained from a Mulliken population analysis at the B3LYP/6-31G** level with the Gaussian0327 suite of programs. B. Molecular Dynamics Simulations. All simulations (i.e., pure water solvent, water-acetonitrile mixture, and the silica surface in solvent box) were performed with the same protocol. To relieve local strain, the systems were subjected to 100 steps of energy minimization using the Adopted Basis NewtonRaphson algorithm.25 Next, MD simulations were carried out at constant volume and constant temperature using the CHARMM program25 and the CHARMM22 force field.28 The time step in all simulations was 1 fs, and SHAKE29 was used to constrain the water and acetonitrile hydrogen atoms, with the hydrogen atoms of the acridine molecule free to move. Nonbonded interactions were truncated at a distance of 8 Å on an atomby-atom basis using a shift function for the electrostatic interactions and a switch algorithm for the van der Waals interactions. To validate this rather short cutoff, additional simulations were carried out with a longer 10 Å cutoff. In a first step, the systems were heated and equilibrated for 20 ps, then 1 ns of production MD simulations followed. All simulations were carried out with protonated (NH+ form) and unprotonated acridine (N form). The atomic positions of the bulk quartz surfaces (with the exception of the exposed hydrogen atoms of the silanol groups) were held fixed during the simulation (1664 atoms). The atomic coordinates of the MD simulation models were recorded at 50 fs intervals for analysis.
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C. Analysis of the Trajectories. Following the MD simulation, selected structural parameters were determined from averaging over 20 000 structures (coordinates were recorded every 50 fs) over a total of 1 ns to characterize the chromatographic system. The parameters include the alkylsilane chain length; the solvent density; the acridine position; and its diffusion coefficient, D, which is calculated from the Einstein relation30
D)
〈|b r i(t) - b r i(0)|2〉 6t
(2.1)
where b ri(t) is the position of the center of mass of a single molecule, and from the velocity autocorrelation function,
D)
1 3
∫0∞ 〈Vbi(t)‚Vbi(0)〉
(2.2)
where b Vi(t) is the center of mass velocity of molecule i. III. Results A. Solvent Mixture without the Surface. First, the behavior of the solvent mixture (water/ACN) is studied without the presence of the chromatographic interface. The density of the solvent along the z axis is shown in Figure 3a and b for two water/ACN mixtures of 0.2 and 0.5 volumic fraction of ACN, respectively. This corresponds to 0.08 and 0.26 mole fraction of ACN. The density, F, of the solvent,
F)
nS nid S
(3.1)
is calculated from the number of solvent molecules, nS, (water or ACN) in a slab of 1 Å width relative to the number of solvent molecules in the same slab for an ideal, homogeneous mixture, nid S . The density of solvent molecules shown in the graphs is averaged over the last 100 ps, that is, from 900 to 1000 ps. For both mixtures, a high density of one component is balanced by a low density of the other component. This is typical of a microheterogeneous structure in which self-association of solvent molecules of the same types is found. The present finding agrees with continuous microheterogeneity proposed by Reimers and Hall,21 which was investigated by using Raman spectroscopy to study the acetonitrile CN-stretch in aqueous solution to characterize the environment of the acetonitrile molecules. These investigations found that the water/ACN mixture is a continuously evolving system as a function of the ACN molar fraction rather than a system that can be characterized by three structural regions.17 The latter work postulated that water/ACN mixtures show microheterogeneous behavior, that is, formation of aggregates, only for 0.2 e xACN e 0.8, whereas the more recent results of Reimers and Hall suggest that water/ACN mixtures always behave as a microheterogeneous mixture, irrespective of the value of xACN. B. Characterization of the Solvent Mixture, including the Chromatographic Interface. C8 Alkyl Chains. Solvating the alkylsilane surface with the water/ACN mixture leads to a more pronounced heterogeneous structure of the solvent, as shown by the density profiles in Figure 3c and d. Again, the z-axis is along the largest axis of the box, orthogonal to the surface, and its origin is at the position of the oxygen atoms of the silanol group on the surface. The x and y axes are in the plane of the surface. For the present system, ACN concentrates in the middle region of the box, that is, around 35-45 Å for the low and
high ACN fraction mixtures, respectively. The light blue peaks in Figure 3c and d around 4 and 75 Å represent acetonitrile molecules that are localized directly above the surface and intercalate between the alkyl chains. The water molecules accumulate between the top of the alkyl chains and the middle region of the box, that is, 15-35 Å and 45-70 Å. For both fractions of acetonitrile, the same behavior is observed, but it is more pronounced for the high ACN fraction mixture. In the density profile, a peak is also present in the first and last Angstrom slice, which is due to the formation of hydrogen bonds between water and dangling silanol groups. The solvent density profiles are symmetric with respect to the middle of the box. Due to the random position of the alkyl chains on the lower and on the upper silica surface, the lower half z-value of the density profiles is not the exact mirror image of the upper half z-value but displays the same features. C18 Alkyl Chains. The solvent density profiles (Figure 3e and f) display the same features as for C8 alkyl chains except that the acetonitrile molecules do not concentrate in the middle of the simulation box because of the increase in the length of the alkyl chains. Rather, the ACN accumulates 10 Å above the alkyl chains, and the water molecules, in the 25-55 Å region. The dark blue peaks in the first and last Angstrom slice, which correspond to the H-bonds between penetrating water molecules and dangling silanol groups, are again present. C. Dynamics of Acridine near the Chromatographic Interface. It is of interest to investigate the dynamics of the solute (acridine) depending on its initial position with respect to the surface. This provides information concerning the influence of the microheterogeneous solvent environment on the diffusive behavior of the solute. C8 Alkyl Chain. Figure 4a and b shows the temporal evolution of the distance between acridine and the surface in a 50/50, water/ACN mixture for different initial positions of the solute (4, 17.5, and 25 Å above the surface) and in pure water for five different initial positions of acridine (5, 10, 15, 20, and 40 Å above the surface). The widths of the alkyl chain phase measured as the average distance between all terminal alkyl chain carbon atoms and the silica surface (the oxygen atom of the silanol group) are reported in Table 2. 100/0 Water/Acetonitrile. Solvation of the chromatographic surface with pure water leads essentially to a flat density profile. For the initial position at 5 Å from the surface, the acridine remains near the chromatographic interface in the 5-7 Å region above the silica surface. For initial positions at 10 and 15 Å, the acridine moves toward the surface on a 250 to 450 ps time scale and then localizes in the 5-7 Å region, which is between the alkyl chains. Thus, acridine intercalates into the chromatographic column and removes water molecules. For the initial positions at 20 and 40 Å, the acridine molecule remains far away from the surface. 50/50 Water/Acetonitrile. For this mixture, the acetonitrile molecules concentrate 5 Å above the alkyl chains and in the middle of the simulation box, in the 35-45 Å region, whereas the water molecules concentrate in the 15-35 and 45-70 Å region. For an initial position close to the surface, the acridine molecule diffuses away from the surface but remains between 10 and 15 Å, which is between 2 and 7 Å above the terminal groups of the alkyl chains. For the initial position at 17.5 Å from the surface, the acridine approaches the surface and remains in the 10-15 Å region. This region is an ACN-rich region, as is the 30-40 Å region where the acridine remains when starting from 25 Å, whereas the 17.5 and 25 Å regions are water-rich regions. Overall, it is observed that acridine
Acridine Orange Adsorption at C8,18/H2O/CH3CN
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10211
Figure 3. Average solvent density profiles after 1 ns from the simulations of different systems. The density is given in 80 slices of 1 Å. Top row: solvent box with 20/80 (left) and 50/50 (right) acetonitrile/water mixture. Middle row: chromatographic system with high load of C8 alkyl chains in 20/80 (left) and 50/50 (right) acetonitrile/water mixture. Bottom row: chromatographic system with C18 alkyl chains in a 50/50 acetonitrile/water mixture with low (left) and high (right) coverage.
diffuses away from water-rich regions to acetonitrile-rich regions, which means that acridine transport appears to be driven by the water concentration. It is also of interest to consider the average length of the alkyl chains in the two different solvent mixtures. The solvation of the alkyl chains shortens the alkyl chains from 9.9 Å (which is the fully extended all-trans conformation) to 7.8 Å in the 50/50 water/acetonitrile mixture and 7.2 Å in pure water for a
surface coverage of 2.65 µmol/m2. This agrees qualitatively with previous work by Lippa et al.31 In their all-atom MD simulations of C8 chains in vacuum, they found an average phase thickness of 6.7 Å, for a surface coverage of 2.52 µmol/m2. C18 Alkyl Chains. Figure 4c-f depicts the temporal evolution of the distance between acridine and the surface for six different initial positions of the solute: 5, 10, 15, 20, 30, and 40 Å above the surface and for two different surface coverages (2.65 and
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Figure 4. Evolution of the acridine-surface distance along the time for different initial positions: 5, 10, 15, 20, and 40 Å and for different alkyl chain length, coverage, and acetonitrile/water mixtures. The origin is set at the position of the oxygen atoms of the silanol group on the surface. Top row: high load of C8 alkyl chains in a 50/50 (left) and 0/100 (right) acetonitrile/water mixture. Middle row: low (left) and high (right) load of C18 alkyl chains in 0/100 acetonitrile/water mixture. Bottom row: low (left) and high (right) load of C18 alkyl chains in 50/50 acetonitrile/water mixture.
0.88 µmol/m2) in pure water and in a 50/50 water/acetonitrile mixture, respectively. 100/0 Water/Acetonitrile. For the trajectories with initial positions far from the surface (30 and 40 Å), the acridine molecule remains almost at the same height during the entire simulation. This contrasts with trajectories in which the solute starts close to the surface (10, 15, and 20 Å from the surface).
There, it is observed that the acridine molecule diffuses toward the top of the alkyl chain, independent of the surface coverage. 50/50 Water/Acetonitrile. For a high surface coverage, the acridine molecule diffuses to the top of the alkyl chains, irrespective of its initial positions, except for a starting position very close (5 Å) to the surface. In this case, the acridine molecule intercalates and remains almost at the same position
Acridine Orange Adsorption at C8,18/H2O/CH3CN
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10213
TABLE 2: Alkyl Chain Phase Thickness in Angstroms Defined as the Average Height of the Alkyl Chains with Respect to the Silica Layer in Pure Water and in a 50/50 Water/Acetonitrile Mixture with 0.88 (Low Surface Coverage) and 2.65 µmol/m2 (High Surface Coverage) C8 and C18 Alkyl Chains alkyl chain
surface coverage
C8 C18 C18
2.65 0.88 2.65
average chain lengtha,b pure water 50/50 7.2 ( 0.3 5.5 ( 0.7 12.8 ( 0.6
7.8 ( 0.2 11.7 ( 1.7 14.8 ( 0.7
a Averaged over 1 ns trajectory. b Uncertainty represents standard deviation over 1 ns trajectory.
Figure 6. Angular correlation function of acridine for the vector b x, b y, and b. z
Figure 5. Alkyl chain phase thickness for different surface coverages. Lippa’s work refers to ref 31.
during the simulation. For a starting position at 40 Å above the surface, the acridine molecule also diffuses to the top of the alkyl chains but on a longer time scale (1.240 ns, not shown in Figure 4f). For the trajectories with low surface coverage, the acridine molecule diffuses to the top of the alkyl chains, whatever its initial position. The shortening of the alkyl chains due to solvation is more pronounced for the C18 chain than for the C8 chain. The C18 chain shortens from 22.8 Å (fully extended all-trans conformation) to 14.8 Å in the 50/50 water/ACN mixture and 12.8 Å in pure water. Lippa et al.31 also noticed a change in the extent of the alkyl chains for increasing surface coverage. As the surface coverage increases from 1.71 to 2.46 µmol/m2, the phase thickens from 9.0 Å to 12.5 Å. In the present simulations, the phase thickness of the alkyl chains increases from 5.5 to 12.8 Å, for a surface coverage increase from 0.88 to 2.65 µmol/ m2. The present and literature data are collected in Figure 5. D. Acridine Transport. Characterizing the motion of acridine in the different solvents and at the interface provides valuable atomistic information and is likely to contribute to understanding the retentive process in RPLC. As a validation of the current simulation setup, results on diffusion in pure solvent and reorientation at the surface are reported and compared to experimental data. Then, the diffusion of acridine at the chromatographic interface is studied in some detail. 1. Diffusion in the SolVent Box. As a validation of the present simulation procedure, first the diffusion constant of TIP3P water was determined. The self-diffusion coefficient of water evaluated from the slope of the mean square displacement versus time calculated from averaging over the 721 water molecules is D ) 0.330 ((0.010) × 10-4 cm2/s, which compares well with the experimental value of 0.23 × 10-4 cm2/s from pulsed-
gradient spin-echo NMR experiments.32 Recent computer simulations33 compared bulk properties for five water models (TIP3P original and modified, SPC original and refined, and SPC/E). From MD simulations of 901 water molecules in a cubic box with a side length of 30 Å, they estimated the selfdiffusion coefficients of TIP3P-water at 298 K from eq 2.1 to be 0.578 ((0.010) × 10-4 cm2/s. Using the Einstein relation (cf. equation 2.1) for the diffusion coefficient of protonated and unprotonated acridine in water, averaging over 10 independent simulations in a 28 × 28 × 28 Å water box yields D ) 0.083 ((0.014) × 10-4 and D ) 0.087 ((0.018) × 10-4 cm2/s, respectively. From the velocity autocorrelation function (eq 2.2), these diffusion coefficients are D ) 0.079 ((0.011) × 10-4 and D ) 0.079 ((0.010) × 10-4 cm2/s. These values compare with the experimental value D ) 0.042 × 10-4 cm2/s.34 The overestimation of D from the simulations compared with experiment by a factor of 2-3 agrees with simulations of pure water described above and data from the literature.33 Thus, the systems setup and the parametrization correctly capture dynamical features such as the diffusion constant. 2. Acridine Reorientation. Experimentally, the reorientation of acridine at the chromatographic surface has been investigated using fluorescence anisotropy spectroscopy.35-37 Reorientation is sensitive to the rotational motion of the solute parallel to the surface and serves as another quantity to validate the present simulations. Experimentally, reorientation was studied for acridine at a C18/water interface. The 1 ns MD simulation for the silica layer with C8 alkyl chains solvated in water with acridine initially located 5 Å from the silica surface was used for the determination of the reorientation. The angular correlation function of the acridine molecule is calculated as
rθ(t) ) 〈∆θ(t)2〉
(3.2)
where ∆θ(t) is the angle of rotation of the molecule during time t, and the brackets, 〈〉, are an average over the initial position. Thus, the reorientation angle between the two acridine structures is calculated in a root-mean-square sense. This angular correlation function was calculated for all spatial dimensions b x, b y, and b. z In the acridine molecular frame, the orthogonal directions b x, b y, and b z are defined as follows: b x ) N1C B7 X C4C B9, b y ) C4C B9, and b z ) N1C B7 (cf. Figure 2). Figure 6 shows the reorientation rθ(t) of acridine in time. The reorientation around directions b x and b y is clearly correlated, as can be seen from their similar
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TABLE 3: Diffusion Coefficient (× 10-4 cm2/s) of Acridine (NH+ and N Forms) Calculated for Different Initial Positions in Pure Water and in 50/50 Water/Acetonitrile Mixture with 0.88 (Low Surface Coverage) and 2.65 µmol/m 2 (High Surface Coverage) of C8 and C18 Alkyl Chains C8 initial position (Å)
C18
low 0/100
high 50/50
low
high
0/100
50/50
0/100
50/50
0/100
50/50
0.022 ( 0.014 0.025 ( 0.017 0.069 ( 0.042 0.075 ( 0.014 0.096 ( 0.015 0.100 ( 0.017
0.030 ( 0.018 0.052 ( 0.018 0.052 ( 0.011 0.056 ( 0.018 0.062 ( 0.011 0.089 ( 0.019
0.008 ( 0.004 0.020 ( 0.011 0.019 ( 0.013 0.032 ( 0.011 0.066 ( 0.025 0.085 ( 0.017
0.008 ( 0.003 0.026 ( 0.015 0.031 ( 0.011 0.032 ( 0.009 0.052 ( 0.011 0.051 ( 0.018
0.013 0.026 0.088 0.087 0.119 0.126
0.039 0.041 0.070 0.075 0.069 0.106
0.013 0.025 0.077 0.036 0.060 0.061
0.005 0.028 0.003 0.023 0.040 0.069
5 10 15 20 30 40
0.032 ( 0.013 0.039 ( 0.016 0.076 ( 0.043 0.093 ( 0.025 0.105 ( 0.023 0.121 ( 0.042
0.061 ( 0.018 0.083 ( 0.024 0.088 ( 0.022 0.093 ( 0.029 0.122 ( 0.023 0.117 ( 0.028
0.016 ( 0.009 0.015 ( 0.010 0.041 ( 0.020 0.083 ( 0.034 0.114 ( 0.033 0.122 ( 0.027
N Form 0.024 ( 0.021 0.048 ( 0.011 0.079 ( 0.033 0.076 ( 0.031 0.100 ( 0.020 0.113 ( 0.016
5 10 15 20 30 40
0.017 0.029 0.047 0.126 0.103 0.096
0.132 0.067 0.063 0.091 0.139 0.103
0.005 0.014 0.054 0.135 0.112 0.124
NH+ Form 0.047 0.114 0.077 0.122 0.127 0.094
TABLE 4: Lateral Diffusion Coefficient (× 10-4 cm2/s) of Acridine (NH + and N Forms) Calculated for Different Initial Positions in Pure Water and in 50/50 Water/acetonitrile Mixture with 0.88 (low Surface Coverage) and 2.65 µ Mol/m2 (high Surface Coverage) of C8 and C18 Alkyl Chains C8 initial position (Å)
C18
low 0/100
high 50/50
low
high
0/100
50/50
0/100
50/50
0/100
50/50
0.028 ( 0.017 0.033 ( 0.022 0.078 ( 0.055 0.087 ( 0.019 0.109 ( 0.017 0.113 ( 0.025
0.036 ( 0.022 0.061 ( 0.021 0.063 ( 0.017 0.062 ( 0.012 0.062 ( 0.018 0.071 ( 0.014
0.009 ( 0.005 0.021 ( 0.013 0.021 ( 0.016 0.036 ( 0.017 0.067 ( 0.033 0.091 ( 0.023
0.008 ( 0.003 0.026 ( 0.017 0.036 ( 0.019 0.038 ( 0.010 0.056 ( 0.016 0.053 ( 0.027
0.010 0.021 0.065 0.069 0.100 0.070
0.033 0.037 0.049 0.064 0.047 0.073
0.010 0.020 0.069 0.033 0.033 0.042
0.004 0.017 0.002 0.010 0.027 0.061
5 10 15 20 30 40
0.044 ( 0.020 0.050 ( 0.021 0.086 ( 0.049 0.086 ( 0.033 0.107 ( 0.033 0.124 ( 0.039
0.068 ( 0.024 0.099 ( 0.034 0.106 ( 0.030 0.107 ( 0.039 0.138 ( 0.042 0.129 ( 0.035
0.023 ( 0.013 0.022 ( 0.014 0.049 ( 0.023 0.097 ( 0.049 0.131 ( 0.046 0.134 ( 0.035
N Form 0.030 ( 0.027 0.058 ( 0.013 0.093 ( 0.041 0.083 ( 0.040 0.119 ( 0.033 0.129 ( 0.028
5 10 15 20 30 40
0.016 0.028 0.039 0.083 0.079 0.057
0.090 0.039 0.056 0.067 0.125 0.090
0.005 0.012 0.039 0.092 0.085 0.099
NH+ Form 0.035 0.079 0.074 0.105 0.104 0.078
double exponential decay behavior with a decay time of 700 ps. Reorientation around b z is uncorrelated. The correlated movement around vectors b x and b y and the large time value before reaching a plateau could be interpreted as a hindered rotation in the silica surface plane. On the contrary, the short time (20 ps) necessary to reach a plateau (rθ(t > 20 ps) ) 0.85) for the reorientation around the vector b z means that the acridine can freely tilt perpendicularly to the silica plane by an angle of acos(r(t > 20 ps))/2 ) 15.9°. This value compares favorably with 18° from the experiments of Wirth and Burbage35 at a C18/ water interface. Experimental decay times for the reorientational correlation function are 740 and 130 ps,35 as compared to 700 and 20 ps from the simulations. The almost quantitative agreement for the slow component is probably fortuitous. More importantly, the simulations correctly distinguish between a slow and a fast component, which differ by ∼1 order of magnitude. 3. Acridine Diffusion. The diffusion coefficients for acridine orange in pure water and in a 50/50 water/acetonitrile mixture for two different coverages of C8 and C18 alkyl chains are collected in Tables 3 and 4. For simulations starting with acridine close to the chromatographic surface, the diffusion coefficients decrease (see Table 3). Initial positions 15, 10, and 5 Å above the surface lead to intercalation of acridine between the alkyl chains, where its movement is hindered and D decreases. Likewise, as the surface coverage increases, D decreases (see Table 3) due to
intercalation. For unprotonated acridine, the error bar for D was calculated from 2 sets of 10 independent, 1 ns trajectories for the C18 system with low coverage (0.88 µmol/m 2). For an initial position at 15 Å, D ) 0.069 ((0.042) × 10-4 cm2/s and for an initial position at 30 Å, D ) 0.096 ((0.015) × 10-4 cm2/s. In the latter case, the trajectories sample similar regions in phase space, and the acridine molecule remains far away from the surface. Only at the end of three trajectories does the acridine approach within 10 Å of the surface. The larger error for the first set of trajectories arises from the fact that in some cases, the acridine interacts with the alkyl chains, whereas for other trajectories, it diffuses away from them. These two sets of trajectories have different diffusion coefficients: a low value of D for acridine close to the surface (D ) 0.022 ((0.003) × 10-4 cm2/s) and a larger value (D ) 0.117 ((0.020) × 10-4 cm2/s) for acridine far away from the surface, which compares well with the 0.096 × 10-4 cm2/s from the 30 Å set. Interestingly, the low value is around 4 times smaller than the one in bulk water. This compares with a factor of 10-35, depending on the data, found experimentally.34-38 IV. Discussion and Conclusion The present work presents all-atom computer simulations of a realistic model for RPLC. To the best of our knowledge, this is the first detailed atomistic simulation that compares the results
Acridine Orange Adsorption at C8,18/H2O/CH3CN with experimental data. The simulation setup consists of two silica surfaces separated by 80 Å with three different alkyl groups (-OH, -CH3, and either (CH2)7-CH3 or (CH2)17-CH3) tethered to them and solvated in different acetonitrile/water mixtures. Two different, experimentally relevant surface coverages together with two solvent environments (pure water and 50/50 acetonitrile/water mixture) were studied. It is observed that the silica surface with the different alkyl groups repel the water molecules because of the hydrophobicity of the alkyl chains. To validate the utility of a molecular dynamics approach to understanding the physical chemistry in RPLC, experimentally observable quantities, such as the diffusion coefficient and the reorientational time of the acridine molecule and properties of the column itself (e.g., thickness of the stationary phase), were calculated. For all except for one quantity (see below), favorable agreement between experiment and simulations was found. The calculated diffusion coefficients for acridine in pure water, excluding the silica surface, differ from the experimental value by only a factor of 2. For the lateral acridine diffusion coefficient at the water/C18 interface, a value 4 times smaller than its diffusion coefficient in bulk water is found. This compares with a factor of 35 measured by fluorescence-recovery after photobleaching by Zulli et al.34 The only appreciable difference between experiment and the current simulations concerns the behavior of D as a function of the surface coverage of the alkyl chains. For surface coverages of 0.88 and 2.65 µmol/m,2 the simulations find a decrease in the acridine diffusion coefficient (from 0.077 to 0.035 × 10-4 cm2/s) whereas experimentally,38 the opposite behavior is observed (increase from 0.000 11 to 0.003 50 × 10-4 cm2/s for surface coverage of 0.8-2.9 µmol/m2). The latter is rationalized by a decrease in contiguity of the hydrocarbon layer as the coverage is lowered. Consequently, acridine should be able to diffuse to the silica surface, where its diffusion is slow. However, this explanation contrasts with results from spectroscopic experiments (Fourier transform infrared39 and Raman;40 for a study that found similar conformational ordering with different C18 densities, see ref 41) and simulation studies that found that for low surface coverage, the conformational order for C18 chains is decreased, and the chains tend to be oriented parallel to the surface.31 This effectively protects the silica surface from interacting with the solute. The opposite trends for D as a function of the surface coverage warrant further computational and experimental investigations. It will be particularly interesting to investigate acridine diffusion in columns with different functionalizations of the alkyl chains. The relative changes should help to clarify whether details in the force field parametrization lead to the observed discrepancy. In this regard, it is also of interest to consider uncertainties from experimental work. As an example, two independent measurements34,38 for virtually identical surface coverages of 3.0 and 2.9 µmol/m2 lead to quite different diffusion coefficients, namely D ) 0.0013 and D ) 0.0035 × 10-4 cm2/s, respectively. In a previous Monte Carlo simulation study of a dimethyl octadecyl/silica system in neat water with a united-atom forcefield, Zhang et al.42 already noticed the depletion of the number of water molecules just above the surface and between the alkyl chains. The natural behavior of the acetonitrile/water mixtures to self-associate2 with the same type of molecules induced an increase in acetonitrile molecules on top and below this water aggregate, that is, in the middle of the simulation box and between the alkyl chains. On the time scale considered in the present work (nanoseconds) the all-atom simulations suggest that the transport of the
J. Phys. Chem. B, Vol. 111, No. 34, 2007 10215 acridine molecule is not exclusively and directly governed by the surface coverage itself, but rather, by the solvent distribution above the functionalized surface. This distribution is, in turn, largely determined and directly driven by the surface (which consists of the silica layer and the alkyl chains including their functionalization). As seen in this study, the solvent distribution changes when the alkyl chains were shortened from C18 to C8. Thus, it is expected that other functionalizations (e.g., -CN, -NH2) of the terminal group will lead to a modified solvent distribution which, in turn, leads to different transport behavior and retention times of the acridine molecule. Given this finding, the explicit inclusion of the solvent in the simulations of mobility and retention studies of small molecules is necessary for meaningful results. Acknowledgment. M.M. acknowledges financial support from the Schweizerischer Nationalfonds through a Fo¨rderungsprofessur. Part of this work was supported by Pfizer, Inc. References and Notes (1) Eaton, G.; Pena-Nunez, A. S.; Symons, M. C. R. J. Chem. Soc. Faraday Trans. 1988, 84, 2181. (2) Jamroz, D.; Stangret, J.; Lindgren, J. J. Am. Chem. Soc. 1993, 115, 6165. (3) Takamuku, T.; Tabata, M.; Yamaguchi, A.; Nishimoto, J.; Kumamoto, M.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998, 102, 880. (4) Venables, D. S.; Schmuttenmaer, C. A. J. Chem. Phys. 1998, 12, 4935. (5) Venables, D. S.; Schmuttenmaer, C. A. J. Chem. Phys. 2000, 24, 11222. (6) Kabisch, G. V. Z. Phys. Chem. 1982, 263, 48. (7) Rowlen, K. L.; Harris, J. M. Anal. Chem. 1991, 63, 964. (8) Balakrishnan, S.; Easteal, A. 1981, 34, 943. (9) Nigam, S.; Juan, A. D.; Stubbs, R. J.; Rutan, S. C. Anal. Chem. 2000, 72, 1956. (10) Goldammer, E. V.; Hertz, H. G. J. Phys. Chem. 1970, 74, 3734. (11) Easteal, A. J. Aust. J. Chem. 1979, 32, 1379. (12) Leiter, H.; Patil, K. J.; Hertz, H. G. J. Solution Chem. 1983, 12, 503. (13) Leiter, H.; Albayrak, C.; Hertz, H. G. J. Mol. Liq. 1984, 27, 211. (14) Hardy, E. H.; Zygar, A.; Zeidler, M. D. Z. Phys. Chem. 2000, 214, 1633. (15) Dawson, E. D.; Wallen, S. L. J. Am. Chem. Soc. 2002, 124, 14210. (16) Naberukhin, Y. I.; Rogov, A. Russ. Chem. ReV. 1971, 40, 207. (17) Moreau, C.; Douhe´ret, G. J. Chim. Phys. 1974, 71, 1313. (18) Kovacs, H.; Laaksonen, A. J. Am. Chem. Soc. 1991, 113, 5596. (19) Marcus, Y.; Mignon, Y. J. Phys. Chem. 1991, 95, 400. (20) Mountain, R. D. J. Phys. Chem. A 1999, 103, 10744. (21) Reimers, J. R.; Hall, L. E. J. Am. Chem. Soc. 1999, 121, 3730. (22) Gritti, F.; Guiochon, G. J. Chromatogr., A 2006, 1103, 69. (23) Snyder, L. R.; Dolan, J. W.; Carr, P. W. J. Chromatogr., A 2004, 1060, 77. (24) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (25) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comp. Chem. 1983, 4, 187. (26) Herzberg, G. Electronic spectra and electronic structure of polyatomic molecules; Van Nostrand: New York, 1966. (27) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.01; Gaussian, Inc.: Wallingford CT, 2004. (28) MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.;
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