Structure and aggregation in model tetramethylurea solutions Rini Gupta and G. N. Patey Citation: The Journal of Chemical Physics 141, 064502 (2014); doi: 10.1063/1.4892411 View online: http://dx.doi.org/10.1063/1.4892411 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydrophobic hydration driven self-assembly of curcumin in water: Similarities to nucleation and growth under large metastability, and an analysis of water dynamics at heterogeneous surfaces J. Chem. Phys. 141, 18C501 (2014); 10.1063/1.4895539 C60-dyad aggregates: Self-organized structures in aqueous solutions J. Chem. Phys. 141, 144303 (2014); 10.1063/1.4896559 Aggregation in dilute aqueous tert-butyl alcohol solutions: Insights from large-scale simulations J. Chem. Phys. 137, 034509 (2012); 10.1063/1.4731248 Aggregation work at polydisperse micellization: Ideal solution and “dressed micelle” models comparing to molecular dynamics simulations J. Chem. Phys. 133, 244109 (2010); 10.1063/1.3519815 Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions J. Chem. Phys. 121, 6986 (2004); 10.1063/1.1790831
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THE JOURNAL OF CHEMICAL PHYSICS 141, 064502 (2014)
Structure and aggregation in model tetramethylurea solutions Rini Gupta and G. N. Pateya) Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
(Received 18 February 2014; accepted 25 July 2014; published online 13 August 2014) The structure of model aqueous tetramethylurea (TMU) solutions is investigated employing largescale (32 000, 64 000 particles) molecular dynamics simulations. Results are reported for TMU mole fractions, Xt , ranging from infinite dilution up to 0.07, and for two temperatures, 300 and 330 K. Two existing force fields for TMU-water solutions are considered. These are the GROMOS 53A6 united-atom TMU model combined with SPC/E water [TMU(GROMOS-UA)/W(SPC/E)], and the more frequently employed AMBER03 all-atom force field for TMU combined with the TIP3P water model [TMU(AMBER-AA)/W(TIP3P)]. It is shown that TMU has a tendency towards aggregation for both models considered, but the tendency is significantly stronger for the [TMU(AMBERAA)/W(TIP3P)] force field. For this model signs of aggregation are detected at Xt = 0.005, aggregation is a well established feature of the solution at Xt = 0.02, and the aggregates increase further in size with increasing concentration. This is in agreement with at least some experimental studies, which report signals of aggregation in the low concentration regime. The TMU aggregates exhibit little structure and are simply loosely ordered, TMU-rich regions of solution. The [TMU(GROMOSUA)/W(SPC/E)] model shows strong signs of aggregation only at higher concentrations (Xt 0.04), and the aggregates appear more loosely ordered, and less well-defined than those occurring in the [TMU(AMBER-AA)/W(TIP3P)] system. For both models, TMU aggregation increases when the temperature is increased from 300 to 330 K, consistent with an underlying entropy driven, hydrophobic interaction mechanism. At Xt = 0.07, the extra-molecular correlation length expected for microheterogeneous solutions has become comparable with the size of the simulation cell for both models considered, indicating that even the systems simulated here are sufficiently large only at low concentrations. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892411] I. INTRODUCTION
Tetramethylurea (TMU) is an amphiphilic molecule, which at room temperature is water soluble at all proportions. Aqueous TMU solutions can serve as excellent solvents for many substances,1, 2 as useful media for chemical reactions,2 and are widely used as a strong denaturing agent for polypeptides and protein.3–5 Given these applications, there is a good deal of current interest in acquiring a detailed understanding of the microscopic structure of TMU solutions, particularly focusing on possible solute aggregation. Aqueous TMU solutions have been the subject of a considerable number of experimental6–28 and theoretical29–35 (computer simulation) studies. Unusual features at relatively low TMU mole fractions (Xt ) have been reported for a variety of experimentally measured properties. For example, at 300 K volumetric properties6 exhibit extrema at Xt ≈ 0.055, the heat of mixing10 has a maximum at Xt ≈ 0.07, and the azeotropic vapour pressure12 shows maxima over the concentration range Xt = 0.03–0.067, depending on the temperature. These effects are generally attributed to some form of hydrophobic hydration involving the methyl groups of TMU. Koga and co-workers13 have also observed extrema and other features at comparable TMU concentrations in higher derivatives of thermodynamic functions, and interpret their findings a)
[email protected] 0021-9606/2014/141(6)/064502/10/$30.00
in terms of different “mixing schemes” becoming operational as Xt increases. There are also experimental studies that detect solute association driven by hydrophobic interactions amongst TMU molecules.14, 15, 23, 25, 27 The structure of dilute aqueous TMU solutions has been investigated using small angle neutron scattering22–27 (SANS) and small angle X-ray scattering27, 28 (SAXS) techniques. These investigations revealed a number of anomalies such as a maximum in the radius of gyration23, 25, 27 at low TMU concentration and slow diffusion22 of water molecules, that indicate some kind of structural change in the water-rich region of solution. Some of these investigations23, 25, 27 provide evidence of attractive solute-solute interactions beginning at low concentrations. For example, recent SANS experiments27 support TMU aggregation in the concentration range 0.0125 ≤ Xt ≤ 0.025. Moreover, the underlying solute-solute attractions increase with increasing temperature, strongly suggesting that they are of hydrophobic origin. However, some experimental studies28 did not find evidence for solute aggregation in the water-rich region (Xt < 0.06). There have been a number of simulation investigations involving model TMU-water systems.29–35 Most of this work has focused on the structural and dynamical properties of water in the first solvation shell of a TMU molecule, but some attention has been paid to possible TMU aggregation,34 and to the influence of TMU on the denaturation of model
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proteins.33 We note that recent simulations34 of concentrated TMU-water solutions do report significant TMU aggregation. However, the properties of the aggregates and the nature of the microheterogeneity in TMU-water solutions are not well understood, and this is true even of dilute solutions where very large systems can be required to accommodate the long, extra-molecular correlation lengths associated with aggregation.36–38 Previous simulations of TMU-water solutions have been limited to a few hundred, or a few thousand molecules, and while relatively small systems might suffice for determining the short-range TMU-water structure, they may not be sufficient to properly capture solute aggregation. In earlier simulations of dilute 2-butoxyethanol (2BE)water36, 37 and t-butanol (TBA)-water38 solutions, we found that in order to obtain a clear picture of solute aggregation and the associated length scales, sample sizes of at least 32 000 molecules, and simulation runs of at least several tens of nanoseconds, were required. Another important issue is that sensitivities to the particular force field employed, such as whether or not demixing occurs, can be masked by finite-size effects in small systems.38 The present paper is a contribution to the continuing effort to understand aqueous TMU solutions. We investigate TMU-water mixtures using large-scale MD simulations (32 000 and 64 000 molecules) focusing on TMU aggregation and microheterogeneity in dilute solutions. We consider concentrations ranging from infinite dilution to Xt = 0.07, and compare results obtained with two different force fields. We find that large systems are indeed necessary to address TMU aggregation in this concentration regime. We also demonstrate that the solute aggregation is sensitive to the force field employed, and that force field variations, especially the modeling of TMU, can lead to significantly different aggregation tendencies. By showing that the aggregation of TMU tends to increase with increasing temperature, we confirm that hydrophobic interactions underly the forces driving TMU association. Additionally, our simulations give a good deal of insight into the physical nature of the TMU aggregates. The remainder of this paper has the following organization. The models and simulation method are described in Sec. II, the results are presented and discussed in Sec. III, and our main conclusions are summarized in Sec. IV. II. MODELS AND SIMULATION METHOD
In order to obtain some assessment of possible model dependence, molecular dynamics simulations were carried out with two different force fields. In one set of calculations the AMBER03 force field39 for TMU is combined with the TIP3P water model,40 and in the other the GROMOS 53A6 model41 for TMU is used together with SPC/E water model.42 The AMBER03 force field is an all-atom model, whereas in GROMOS 53A6 the methyl groups of TMU are represented by a united-atom approximation, where the hydrogen atoms are not considered explicitly. For convenience, we refer to these force fields as TMU(AMBER-AA)/W(TIP3P) and TMU(GROMOS-UA)/W(SPC/E), respectively. We note that the AMBER force field in combination with TIP3P water is widely used in simulations of biological systems.33 In all
J. Chem. Phys. 141, 064502 (2014) TABLE I. Lennard-Jones parameters and partial charges for the models considered. Atom Water (SPC/E) O H Water (TIP3P) O H TMU (GROMOS-UA) C (carbonyl) O (carbonyl) C (methyl) N TMU (AMBER-AA) C (carbonyl) O (carbonyl) C (methyl) N H (alkyl groups)
σ (Å)
(kJ/mol)
Charge (e)
3.166 0.0
0.6501 0.0
− 0.8476 0.4238
3.1505 0.0
0.63638 0.0
− 0.834 0.417
3.5812 2.7601 3.7494 3.5722
0.27741 1.2791 0.8671 0.2931
0.599 − 0.607 0.058 − 0.112
3.3996 2.9599 3.3996 3.25 2.4713
0.3598 0.8786 0.4577 0.7112 0.06568
0.7623 − 0.6045 − 0.1871 − 0.2471 0.0904
molecular models considered, the bond lengths and angles are held fixed. All site-site interactions are described by LennardJones (LJ) and/or Coulombic potentials. The LJ cross interactions are obtained via the usual Lorentz-Berthelot combining rules. The interaction parameters are summarized in Table I. The atomic partial charges employed in the AMBER TMU model were obtained using the R.E.D (RESP ESP charge Derive Server) server,43 and were derived according to the restrained electrostatic potential (RESP) model44 for charge generation. All AMBER format topology files were converted from AMBER to GROMACS format using the FFAMBER tools script.45 All MD simulations were performed employing GROMACS46, 47 version 4.5.5 (double precision). The equations of motion are integrated using the leapfrog algorithm (timestep of 1 fs). The molecules are kept rigid by applying constraints to the interatomic distances within a molecule, using the LINCS52 algorithm. The LJ interactions are spherically truncated at 0.9 nm. The Coulombic interactions are obtained using the particle mesh Ewald (PME) method;48, 49 the real space interactions are evaluated using a 0.9 nm cutoff, and the reciprocal space interactions are calculated on a 0.12 nm grid with fourth order cubic spline interpolation. All simulations were performed in the NPT ensemble at a pressure of 1 atm. Results are reported for two temperatures, 300 and 330 K. The temperature is controlled using a velocity rescaling algorithm50 (τ t = 0.1 ps), and the pressure by applying the Berendsen coupling method51 (τ p = 1 ps). Initial configurations were obtained by minimizing the energy of water and TMU molecules confined in a cubical box. The initial box sizes were determined from the experimental densities of TMU-water solutions.6–8 All systems were relaxed for 2 ns, followed by production runs of 30 ns. As noted above, in order to investigate association and microheterogeneity by simulation, it is necessary to use systems that are large enough to accommodate aggregates, and the resulting correlation lengths. Therefore, simulation results are reported for 32 000 molecules (water plus TMU) for
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J. Chem. Phys. 141, 064502 (2014)
TMU(AMBER-AA)/W(TIP3P), and for 64 000 molecules for TMU(GROMOS-UA)/W(SPC/E). Note that the larger 64 000 molecule system was not computationally feasible for the AMBER all-atom model for TMU. Solutions varying in TMU concentration from infinite dilution up to a mole fraction Xt = 0.07 are considered. III. RESULTS AND DISCUSSION
In order to gain a qualitative overview of aggregation and microheterogeneity in TMU-water mixture models, it is useful to consider configurational snapshots for a range of concentrations. Snapshots for the TMU(AMBER-AA)/ W(TIP3P) model at Xt = 0.005, 0.02, and 0.07 are shown in Fig. 1, and corresponding snapshots for TMU(GROMOS-
FIG. 2. Configurational snapshots of TMU-water solutions for the TMU(GROMOS-UA)/W(SPC/E) model with 64 000 particles. From top to bottom the panels are Xt = 0.005, Xt = 0.02, and Xt = 0.07. The colors are as in Fig. 1 except that the methyl hydrogen atoms (green) are absent in this model.
FIG. 1. Configurational snapshots of TMU-water solutions for the TMU(AMBER-AA)/W(TIP3P) model with 32 000 particles. The water molecules are pink and the TMU molecules are shown as: carbon atoms (black), nitrogen atoms (blue), oxygen atoms (red), and methyl hydrogen atoms (green). From top to bottom the panels are Xt = 0.005, Xt = 0.02, and Xt = 0.07.
UA)/W(SPC/E) in Fig. 2. For the TMU(AMBERAA)/W(TIP3P) model (Fig. 1), one can detect signs of relatively small TMU aggregates at Xt = 0.005, much larger aggregates at Xt = 0.02, and further aggregation or possibly phase separation at Xt = 0.07. The situation for the TMU(GROMOS-UA)/W(SPC/E) model (Fig. 2) is somewhat different. For this model there is little if any TMU aggregation at Xt = 0.005, traces of aggregation at Xt = 0.02, and increased aggregation as the concentration is increased to Xt = 0.07. For both models the TMU aggregates do not have well-defined, micelle-like structures. Rather, the microheterogeneity appears to consist of TMU-rich and water-rich patches with the TMU-rich patches growing in size with increasing concentration. This physical picture is
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J. Chem. Phys. 141, 064502 (2014) TMU(AMBER-AA)/W(TIP3P) Xt=0.0
0.4 (a)
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FIG. 3. An expanded configurational snapshot for the TMU(AMBERAA)/W(TIP3P) model with 32 000 particles at Xt = 0.04. Only water molecules within 4 Å of a TMU molecule are shown. The colors are as in Fig. 1.
P(N)
0.6 0.4 0.2 0
further supported by the expanded view snapshot shown in Fig. 3 for the TMU(AMBER-AA)/W(TIP3P) model at Xt = 0.04. Note that in this snapshot only water molecules within 4 Å of a TMU molecule are included, and one can see that many water molecules remain within the TMU-rich regions. Qualitatively, this behavior is similar to our previous observations for TBA-water solutions38 and differs from the 2BE-water case, where better defined more micelle-like aggregates are found.36, 37 Another qualitative observation from Figs. 1 and 2 is that at Xt = 0.07 the length scale of the aggregates is approaching the size of the simulation cell, and that this is particularly true for the TMU(AMBERAA)/W(TIP3P) model (Fig. 1). This point and its relation to possible demixing behavior is further discussed below. We next turn to a more quantitative analysis of TMU aggregation and model comparison. It is useful to begin with normalized probability distribution functions, P(N), which give the probability of finding N water or TMU molecules within the first solvation shell of a given TMU molecule. Such functions for the TMU(AMBER-AA)/W(TIP3P) and TMU(GROMOS-UA)/W(SPC/E) models are shown in Figs. 4 and 5, respectively. TMU-water distributions are given for two TMU sites, specifically, a methyl carbon atom and a nitrogen atom. For TMU-TMU distributions methyl carbon atoms are used. These atoms are selected because the dehydration of the hydrophobic parts of TMU is a good indication of aggregation. Also, taken together, the TMU-water and TMU-TMU distributions provide insight into the nature of the aggregates, such as the frequency of methyl-methyl (hydrophobic) “contacts.” The cutoff radius defining the first shell used in calculating a particular P(N) is taken to be the first minimum in the appropriate TMU-water or TMU-TMU
0
1
2
3 N
4
5
6
FIG. 4. Selected probability distributions P(N) for the TMU(AMBER-AA)/ W(TIP3P) model (32 000 particles).
radial distribution function (rdf). For example, the cutoff used to obtain the probability of finding a water oxygen atom (Ow ) within the first shell of a TMU methyl carbon (CH3 ) is obtained from the CH3 –Ow rdf. The rdfs are discussed in detail below. Note that in this paper particular atoms are designated as follows: CH3 , a methyl carbon atom of TMU (methyl group for a united-atom model); Nt , a nitrogen atom of TMU; Ot , the carbonyl oxygen atom of TMU; Ct , the carbonyl carbon atom of TMU; Ow , the oxygen atom of water; and Hw , the hydrogen atom of water. For the TMU(AMBER-AA)/W(TIP3P) model (Fig. 4), we see immediately that the distribution of water around TMU changes rather dramatically as the concentration is increased, with similar stories told from the methyl carbon atom (top panel) and nitrogen atom (middle panel) perspectives. Focusing on the methyl carbon atom (top panel), one notes that the probability distribution has a fairly broad, but welldefined, peak centered at N ≈ 14. At Xt = 0.005, the peak has become noticeably broader, and the probability of finding fewer water molecules in the first solvation shell has become significantly more favorable. This trend continues as Xt increases, and by Xt = 0.02, the distribution is very broad with a maximum at N ≈ 4. At Xt = 0.07, the distribution has become sharper with a maximum at Xt ≈ 3, but there remains a persistent “tail” stretching to higher values of N. A consistent picture is obtained if one considers a nitrogen atom of TMU (middle panel). In that case, the probability maximum
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R. Gupta and G. N. Patey TMU(GROMOS-UA)/W(SPC/E)
0.4
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J. Chem. Phys. 141, 064502 (2014)
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FIG. 5. Selected probability distributions P(N) for the TMU(GROMOSUA)/W(SPC/E) model (64 000 particles).
We also note (Fig. 5, bottom panel) that a higher percentage of TMU methyl groups have no methyl group neighbors than the TMU(AMBER-AA)/W(TIP3P) model at the same concentration. These results indicate that the TMU(GROMOSUA)/W(SPC/E) model has less tendency to aggregate than the TMU(AMBER-AA)/W(TIP3P) force field. This is consistent with the qualitative picture one obtains from the configurational snapshots discussed above. We note that the aggregation properties of the TMU(AMBER-AA)/W(TIP3P) force field appear to be in better qualitative agreement with experimental observations,23, 25, 27 than the TMU(GROMOS-UA)/ W(SPC/E) force field which exhibits a weaker tendency towards aggregation at low concentrations. Therefore, in the following discussion we focus mainly on results obtained for the TMU(AMBER-AA)/W(TIP3P) model, but we do make further comparisons with TMU(GROMOS-UA)/W(SPC/E) results when appropriate. Another sensitive measure of TMU aggregation, and particularly of the associated length scales, is provided by rdfs [g(r)] and related quantities. We have calculated and examined atom-atom rdfs for all possible solute-solvent, solutesolute, and solvent-solvent pairs, but here we only explicitly consider selected rdfs which are especially useful reporters of TMU aggregation. Three selected TMU-water rdfs are plotted in Fig. 6 for a range of concentrations. We note that for all three TMU atoms considered, the general structural features of the rdfs do not change significantly with increasing concentration, indicating that the basic arrangement of water
4
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drops from ∼21 water molecules at infinite dilution, to ∼6 at Xt = 0.02, and ∼5 at Xt = 0.07. This behavior indicates that TMU aggregation begins at a low concentration (Xt 0.005), proceeds rapidly as Xt increases from 0.01 to 0.02, and then continues at a slower rate with increasing Xt . Note that for CH3 –Ow and Nt –Ow , the peaks in P(N) cross over from “high” N values for Xt 0.01 to “low” N values for Xt 0.02. This aggregation picture is confirmed by the P(N) for CH3 –CH3 (Fig. 4, bottom panel), which shows that the fraction of TMU methyl groups without a methyl group of another TMU molecule in its first solvation shell drops from ∼70% at Xt = 0.005 to ∼18% at Xt = 0.02. We note that our observations for the TMU(AMBERAA)/W(TIP3P) model, particularly the crossover behavior of P(N) at Xt ≈ 0.02, are consistent with earlier studies,23, 25, 27 which report some sort of structural change in TMU solutions at or near this concentration. For the TMU(GROMOS-UA)/W(SPC/E) force field, we see from Fig. 5 that the CH3 –Ow (top panel) and Nt –Ow (middle panel) distributions are very similar to the TMU(AMBERAA)/W(TIP3P) case at infinite dilution. However, as the TMU concentration is increased, the departure of water molecules from the first solvation shell of a TMU methyl group or nitrogen atom is not as pronounced as it is for the TMU(AMBERAA)/W(TIP3P) model. The rather rapid crossover in peak position from high to low N observed at Xt ≈ 0.02 for the TMU(AMBER-AA)/W(TIP3P) force field is not present here.
0
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0
0
10
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r(A) FIG. 6. Selected TMU-water rdfs for the TMU(AMBER-AA)/W(TIP3P) model (32 000 particles).
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R. Gupta and G. N. Patey
Xt=0.03
6 g(r)
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X=0.01 Xt=0.02 Xt=0.04 Xt=0.07
4 2 0
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r(A) FIG. 7. Selected TMU-TMU rdfs for the TMU(AMBER-AA)/W(TIP3P) model (32 000 particles).
molecules about TMU is not strongly concentration dependent. Focusing on the CH3 –Ow rdf, we see that the height of the first peak decreases with increasing concentration from infinite dilution to Xt = 0.005. As the concentration is further increased to Xt = 0.02, the first peak in the CH3 –Ow rdf drops very rapidly, and long-range tails that approach unity slowly from below appear in the rdf. Qualitatively, similar behavior is observed in the other TMU-water rdfs shown in Fig. 6, although the decrease in the height of the first peak is smaller in the Ot –Ow rdf, as one might expect for the more hydrophilic carbonyl oxygen atom. Overall, the behavior of the TMU-water rdfs is consistent with the description of TMU aggregation given above. Initial aggregation of TMU molecules occurs for Xt 0.005 and increases at higher concentrations. Two TMU-TMU rdfs are shown in Fig. 7. For the CH3 – CH3 rdf (top panel), the height of the first peak shows an initial increase as Xt is raised from 0.005 to 0.01, and then continually decreases as Xt is increased further. The concentration dependence of the Ct –Ct rdf (bottom panel) is similar except that in this case there is no initial increase in the Xt = 0.005 to 0.01 region. At higher concentrations both rdfs exhibit longrange tails similar to those found in the TMU-water rdfs, except that in the present case the tails approach unity slowly from above. Long-range tails in practically all rdfs are one defining feature of microheterogeneous solutions,36–38 and are further discussed below. At first sight, the short-range behavior of the TMU-TMU rdfs, with peak heights decreasing with increasing TMU concentration, might appear to be at odds with increasing TMU aggregation. To understand why this is not the case, it is necessary to note that the local TMU density, ρt (r) = ρt g(r) = ρXt g(r), where ρ t is the bulk density of TMU, and ρ = ρt + ρw , ρw being the bulk density of water. Then, noting that at low concentrations ρ is nearly independent of Xt
and considering the CH3 –CH3 rdf, we see that as Xt increases from 0.005 to 0.07, the initial peak in g(r) decreases from ∼7 to ∼3, but the corresponding local density actually increases by a factor of ∼3, consistent with the increasing TMU aggregation. We remark that earlier studies22, 23, 25, 26 of TMU-water mixtures have reported the formation of water-separated TMU pairs at low concentration, which are then replaced by direct TMU-TMU association with increasing TMU concentration. We do observe some water-separated TMU pairs in our model simulations, with small numbers of such species being present at all concentrations considered. However, they are dominated by more complex aggregates involving many more than two TMU molecules, as discussed above. As shown in our earlier work with 2BE-water36, 37 and TBA-water38 solutions, a useful measure of the length scales associated with solute aggregation and microheterogeneity, is provided by the long-range behavior of the rdfs. This gives a clear indication of any length scale that exceeds the range of the usual molecular correlations. In order to magnify any extra-molecular correlations, it is convenient to plot functions of the form r2 h(r), where h(r) = g(r) − 1 is the pair correlation function. Results for water-water correlation functions are plotted in Fig. 8. We note that the first peak of the Ow –Ow rdf grows with increasing TMU concentration [Fig. 8(a)], and the r2 h(r) plots [Fig. 8(b)] clearly show that the rdfs develop long-range tails as the TMU concentration increases. For Xt 0.01, r2 h(r) exhibits oscillatory behavior with wavelengths that are much larger than molecular length scales. This is a clear signal of microheterogeneity. Solute aggregation leads to water-rich and water-poor regions, and the associated density variations are reflected in the correlation functions. We note that the amplitude and wavelength of the oscillations increase with increasing TMU content. The position where 5
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FIG. 8. Water-water rdfs (a) and r2 h(r) plots (b) for the TMU(AMBERAA)/W(TIP3P) model (32 000 particles).
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Xt=0.005 Xt=0.01
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FIG. 9. Plots of r2 h(r) for selected TMU-water (a) and TMU-TMU (b) rdfs for the TMU(AMBER-AA)/W(TIP3P) model (32 000 particles). Results for one TMU(AMBER-AA)/W(SPC/E) system (see legend) are included in (a) and (b) for comparison.
r2 h(r) first crosses zero, rcross , varies from ∼43 Å at Xt = 0.01 to ∼55 Å at Xt = 0.02, and shows small additional increases as Xt rises to 0.07. Plots of r2 h(r) obtained with TMU-water and TMUTMU rdfs are shown in Fig. 9, and the expected oscillatory behavior is obvious. In these functions the long-range, extramolecular correlations first become apparent at Xt ≈ 0.01, are easily discernible at Xt = 0.02, and are strongly pronounced at Xt = 0.03. For Xt > 0.03, the wavelengths approach L/2, and the possible implications of this are discussed below. From Fig. 9, we note that for a particular concentration, the rcross values are similar for both CH3 –Ow and CH3 –CH3 , and that for r < rcross , r2 h(r) is negative for CH3 –Ow and positive for CH3 –CH3 . This indicates TMU aggregates that have a deficit of water and surplus of TMU with respect to the bulk densities, consistent with the qualitative impression given by configurational snapshots. At this point it is appropriate to discuss possible influences of finite sample size on the simulation results. As mentioned above, for the TMU(AMBER-AA)/W(TIP3P) model the aggregate size and associated correlation lengths become comparable with the simulation cell size at higher concentrations (Xt 0.03), and at Xt = 0.07 the system appears to have demixed (see Fig. 1, bottom panel). Similar effects occur for some TBA-water models and, as discussed in our earlier paper,38 there is no unambiguous interpretation of the simulation results at these concentrations. Real TMUwater solutions are known to be miscible at the conditions considered, so demixing-like behavior might indicate problems in the force field employed. Alternatively, such behavior might be an artifact of finite system size coupled with the periodic boundary conditions (PBC) applied in the sim-
ulations. Possibly, stable, finite-size TMU aggregates exist at higher concentrations, but if they are larger than the simulation cell allows, under PBC one observes demixing instead. In principle, this question could be resolved by simulating larger samples, but at present simulations employing the all-atom TMU(AMBER-AA) model are not computationally feasible with more than 32 000 molecules. Given this, a degree of caution should be exercised, when considering the TMU(AMBER-AA)/W(TIP3P) model results for concentrations above Xt = 0.03. To further illustrate sensitivity to force field and possibly to finite sample size, it is useful to consider some r2 h(r) plots for the TMU(GROMOS-UA)/W(SPC/E) model. For this united-atom force field, simulations with 64 000 molecules are feasible, and these are the results we report. In Fig. 10, r2 h(r) plots are shown for CH3 –Ow and CH3 –CH3 . For the TMU(GROMOS-UA)/W(SPC/E) model no long-range correlations are visible for Xt 0.02, consistent with our earlier examination of configurational snapshots (see Fig. 2). At higher concentrations, long-range correlations do develop, they exhibit no oscillatory behavior, but do span the full L/2 cell dimension at Xt = 0.07. The physical structures underlying the long-range correlations appear to be somewhat different for the two models considered. In the TMU(AMBER-AA)/W(TIP3P) case, TMU has a stronger tendency towards association, and aggregation occurs at lower concentrations than it does for TMU(GROMOS-UA)/W(SPC/E). Also, although in both cases the TMU aggregates are very loose without well-defined shape, the segregation of TMU and water is more clearly defined for the TMU(AMBER-AA)/W(TIP3P) force field. For this model the aggregates are sufficiently distinct to produce oscillatory structure in r2 h(r), and demixing-like behavior at higher concentrations. For TMU(GROMOS-UA)/W(SPC/E)
(a)
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J. Chem. Phys. 141, 064502 (2014)
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FIG. 10. Plots of r2 h(r) for selected TMU-water (a) and TMU-TMU (b) rdfs for the TMU(GROMOS-UA)/W(SPC/E) model (64 000 particles).
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064502-8
R. Gupta and G. N. Patey
J. Chem. Phys. 141, 064502 (2014)
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200 0 -200 -400 -600 0 FIG. 11. Configurational snapshot of the TMU(GROMOS-UA)/W(SPC/E) model with 64 000 particles at Xt = 0.07. For clarity water molecules are not shown. The colors are as in Fig. 2.
at Xt = 0.07 (see Fig. 11), there appears to be something closer to a loose “network” of TMU aggregates that spans the cell, and gives rise to the observed long-ranged correlations. As mentioned above, a number of earlier investigations23, 25, 27 have reported the existence of TMU aggregates in the concentration range 0.0125 ≤ Xt ≤ 0.025. These studies suggest that TMU association is due to hydrophobic attraction, which increases with increasing temperature. To gain more insight into the nature of the driving force for TMU association in our model mixtures, additional simulations were carried out at 330 K. Selected r2 h(r) plots (CH3 – Ow and CH3 –CH3 ) for the TMU(AMBER-AA)/W(TIP3P) force field are given in Fig. 12 for two temperatures (300 and 330 K) at Xt = 0.02 and 0.04. These plots clearly show that at both concentrations, both the wavelength and amplitude of the oscillations increase when the temperature is increased from 300 to 330 K. These observations demonstrate the growing tendency of TMU to form larger and denser aggregates as the temperature is increased. This behaviour is characteristic of entropy driven hydrophobic association. A qualitatively similar temperature dependence was found for the TMU(GROMOS-UA)/W(SPC/E) model (plots not shown here). Therefore, despite the differences discussed above, both force fields considered correctly capture the influence of temperature on TMU association. We did perform additional simulations and analysis aimed at obtaining a better understanding of why the TMU(AMBER-AA)/W(TIP3P) and TMU(GROMOS-UA)/ W(SPC/E) force fields exhibit different aggregation behavior. One possibility is that the tendency of TMU to aggregate is sensitive to the different water models employed. To test this possibility, we carried out a simulation for the com-
10
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FIG. 12. Plots of r2 h(r) for selected TMU-water (a) and TMU-TMU (b) rdfs for the TMU(AMBER-AA)/W(TIP3P) model (32 000 particles) at different temperatures.
bination TMU(AMBER-AA)/W(SPC/E) at Xt = 0.04 and 300 K, employing 32 000 molecules. The TMU aggregation in this system was indistinguishable from that observed for TMU(AMBER-AA)/W(TIP3P). This is illustrated in Fig. 9 where we have included results for both TMU(AMBER-AA)/W(TIP3P) and TMU(AMBER-AA)/ W(SPC/E). We note that the curves essentially coincide, effectively ruling out the different water models as the source of the discrepancy. A reasonable alternative explanation is that the aggregation is sensitive to differences in the TMU-water interactions, especially perhaps to the water-carbonyl hydrogen bonding. To examine this possibility, CH3 –Ow , Ct –Ow , and Ot –Hw rdfs obtained for both models at infinite dilution (only a single TMU in the simulation cell) are compared in Fig. 13. From Fig. 13(a), we see that the CH3 –Ow rdfs are very similar for both models. This suggests that the most obvious difference between the models, specifically, GROMOS-UA treats the TMU methyl groups at the united atom level, whereas, the AMBER-AA force field explicitly includes the methyl hydrogen atoms, is likely not the origin of the differing behavior of the models. Similarly, comparing the Ct –Ow rdfs [Fig. 13(b)] does not reveal any large differences in the overall solvation of TMU at infinite dilution, although the initial and second peaks are slightly higher in the TMU(GROMOSUA)/W(SPC/E) rdf. This similar picture of the overall TMU solvation provided by the rdfs is consistent with the similar P(N) plots (Figs. 4 and 5) obtained for both force fields at infinite dilution. However, despite the overall similarities of the TMUwater rdfs at infinite dilution noted above, the Ot –Hw rdfs [Fig. 13(c)] do provide a strong hint of the origin of the different solution behavior. From Fig. 13(c) we notice that
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064502-9
R. Gupta and G. N. Patey
6
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J. Chem. Phys. 141, 064502 (2014)
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r(A) FIG. 13. Comparison of TMU-water rdfs at infinite dilution obtained for the TMU(AMBER-AA)/W(TIP3P) and TMU(GROMOS-UA)/W(SPC/E) models at 300 K.
the first peak in the Ot –Hw rdf for TMU(GROMOS-UA)/ W(SPC/E) is significantly higher than the TMU(AMBERAA)/W(TIP3P) result. This indicates stronger TMU-water hydrogen bonds, which is at least consistent with our observation that TMU has less tendency to aggregate in TMU(GROMOS-UA)/W(SPC/E) solutions than in TMU(AMBER-AA)/W(TIP3P) solutions at the same concentration. Lacking a better (or, indeed, any other) explanation, we believe that it is this relatively small difference in the TMU-water hydrogen bonding that underlies the large qualitative differences in the solution properties of these models. This analysis serves to emphasize that the existence and nature of solute aggregation in aqueous systems can be very sensitive to details of the solute-water interaction. This might also help explain why real aqueous solutions of amphiphilic molecules can exhibit such a wide variety of behavior. IV. SUMMARY AND CONCLUSIONS
Large-scale MD simulations have been used to investigate aggregation and microheterogeneity in dilute TMUwater solutions. Concentrations ranging from Xt = 0 to 0.07, and two temperatures (300 and 330 K) were considered. Simulations were performed for two different models, TMU(AMBER-AA)/W(TIP3P) and TMU(GROMOSUA)/W(SPC/E), in order to make some assessment of the sensitivity to the force field employed. At least qualitatively, the
short-range intermolecular correlations given by both force fields were similar. However, this was not true of the longrange correlations associated with solute aggregation and microheterogeneity. We also show that finite-size effects become a possibly important issue at higher concentrations, complicating the physical interpretation of the simulation results, and making comparisons with experiment somewhat ambiguous. These aspects are similar to our earlier findings for model TBA-water solutions.38 In the TMU(AMBER-AA)/W(TIP3P) case, by examining configurational snapshots, P(N) distributions, and r2 h(r) plots, we first detect evidence of TMU aggregation at Xt = 0.005. This contrasts with the TMU(GROMOSUA)/W(SPC/E) model, where clear signs of TMU aggregation and associated long-range correlations are only evident for Xt ≥ 0.04. For the TMU(AMBER-AA)/W(TIP3P) model, the P(N) for water in the first coordination shell of a TMU methyl group varies rapidly with increasing concentration in the low concentration regime, and the peak position shows a crossover from “large” to “small” N at Xt ≈ 0.02. Slower variations are observed as the concentration is further increased, but basically by Xt = 0.02 the hydrophobic methyl groups have shed a large fraction of their water of hydration. The corresponding CH3 –CH3 probability distribution functions show that much of the water loss from the first coordination shell is being replaced by methyl groups, confirming that the water loss coincides with hydrophobic association. Our simulations also provide a physical picture of the aggregates formed, and of the length scales of the associated microheterogeneity. For the TMU(AMBER-AA)/W(TIP3P) model, configurational snapshots reveal TMU-rich regions with little or no apparent structure. The aggregates or TMU-rich regions lack any micelle-like appearance, but are somewhat similar to the disordered aggregates observed in TBA-water solutions.38 As we have seen for other microheterogeneous solutions,36, 38 the r2 h(r) plots exhibit oscillatory structure roughly related to the “size” of the aggregates, and both the period and amplitude of the oscillations increase as aggregation grows in importance with increasing TMU concentration. For TMU mole fractions higher than 0.04, r2 h(r) functions together with visual inspection of configurational snapshots indicate that the size of the aggregates is approaching the length of the simulation cell. In our periodic geometry configurational snapshots suggest demixing behavior, but it is not possible to determine if this is an unphysical property of the TMU(AMBER-AA)/W(TIP3P) force field, or an artifact of finite system size coupled with periodic boundary conditions. As noted above, the TMU(GROMOS-UA)/W(SPC/E) model shows much less tendency towards aggregation than the TMU(AMBER-AA)/W(TIP3P) force field, but at higher concentrations it too develops long-range correlations that eventually span the size of the simulation cell. It is difficult to reach a firm conclusion as to which of the two force fields considered best represents real TMU-water solutions. However, the tendency of the TMU(AMBER-AA)/W(TIP3P) model to show TMU association at low concentrations appears more consistent with experimental studies27 that suggest TMU aggregation in the same concentration range.
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064502-10
R. Gupta and G. N. Patey
It is difficult to pinpoint exactly why the TMU(AMBERAA)/W(TIP3P) and TMU(GROMOS-UA)/W(SPC/E) force fields exhibit such different aggregation behavior as the TMU concentration is increased. This is especially true given that the solvation of TMU at infinite dilution is quite similar for the two force fields. A simulation using the mixed combination TMU(AMBER-AA)/W(SPC/E) showed that the different water models are definitely not the origin of the discrepancy. We did note that at infinite dilution the TMU-water hydrogen bond is stronger for the TMU(GROMOS-UA)/W(SPC/E) model, and we believe that this is the likely reason why TMU(GROMOS-UA)/W(SPC/E) has a weaker tendency towards aggregation. Our comparison of these two force fields serves to emphasize just how sensitive solute aggregation behavior is to what may appear as relatively small changes in force fields. This is something to be mindful of in simulation studies, and possibly helps explain why real aqueous solutions of small amphiphilic molecules display such varied behavior. Finally, we note that for both models and at all concentrations considered, the aggregation tendency of TMU increases with increasing temperature. This is in agreement with experiment and shows that, despite their differences, aggregation in both models is entropy driven consistent with an underlying hydrophobic mechanism. ACKNOWLEDGMENTS
The financial support of the Natural Science and Engineering Research Council of Canada is gratefully acknowledged. This research has been enabled by the use of WestGrid and Compute/Calcul Canada computing resources, which are funded in part by the Canada Foundation for Innovation, Alberta Innovation and Science, BC Advanced Education, and the participating research institutions. WestGrid and Compute/Calcul Canada equipment is provided by IBM, Hewlett Packard, and SGI. 1 A.
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