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Hydration of “Nonfouling” Functional Groups Jason C. Hower,† Matthew T. Bernards,† Shengfu Chen,† Heng-Kwong Tsao,‡ Yu-Jane Sheng,§ and Shaoyi Jiang*,† Department of Chemical Engineering, UniVersity of Washington, Seattle, Washington 98195; Department of Chemical Engineering, National Central UniVersity, Chung-li, Taiwan 320; and Department of Chemical Engineering, National Taiwan UniVersity, Taipei, Taiwan 106 ReceiVed: July 24, 2008
The prevention of nonspecific protein adsorption to synthetic materials and devices presents a major design challenge in the biomedical community. While some chemical groups can resist nonspecific protein adsorption from simple solutions for limited contact times, there remains a need for new nonfouling functional groups and surface coatings that prevent protein adsorption from complex media like blood or in harsh environments like seawater. Recent studies of the molecular mechanisms of nonfouling surfaces have identified a strong correlation between surface hydration and resistance to nonspecific protein adsorption. In this work, we describe a simple experimental method for evaluating the intrinsic hydration capacity of model surface coating functional groups based on the partial molal volume at infinite dilution. In order to evaluate a range of hydration capacity and nonfouling performance, solutes were selected from three classes: ethylene glycols, sugar alcohols, and glycine analogues. The number of hydrating water molecules bound to a solute was estimated by comparing the molecular volume at infinite dilution to the solute van der Waals molecular volume. The number of water molecules associated with each solute was further validated by constant pressure and temperature molecular dynamics simulations. Finally, a size-normalized molecular volume was correlated to previously observed protein adsorption experiments to relate the intrinsic hydration capacity of functional groups to their known nonfouling abilities. Introduction Surface resistance to nonspecific protein adsorption is important for many applications, including medical implants,1 marine coatings, and biosensors.2 Nonspecific protein adsorption can reduce the performance of medical devices or implanted materials since many undesirable biological cascades are initiated by nonspecific protein adsorption.1-3 Despite extensive studies,4-8 there are still a very limited number of nonfouling materials that meet the various challenges of practical applications, particularly in applications involving complex media such as blood.4,7-9 Thus, the development of nonfouling materials remains an important focus of research. Motivated by the need for new nonfouling materials, many researchers have studied the molecular mechanisms of surface resistance to protein adsorption. Early work with long poly(ethylene glycol) brushes suggested that high chain flexibility was required to prevent protein adsorption via a steric repulsion mechanism.10-13 However, as the length of the polymer brushes and the chain flexibility were decreased, surface hydration became increasingly important.4,6,14-16 Many researchers have proposed that nonfouling surfaces prevent protein adsorption by creating a strong surface hydration layer. The disruption of this strong surface hydration layer leads to a net repulsive force on proteins.4,10,15-20 This proposed mechanism suggests that nonfouling materials and surface coatings must create a strong surface hydration layer to prevent protein adsorption. However, many of the experimental methods for evaluating hydration, * Corresponding author. E-mail:
[email protected]. † University of Washington. ‡ National Central University. § National Taiwan University.
including spectroscopic and calorimetric techniques, are not highly surface sensitive.21 Thus, direct measurement of interfacial hydration water is difficult and often confounded by the bulk water present. The interfacial water and surface hydration are controlled by the intrinsic hydration capacity of the surface functional group and the packing density or surface coverage. In this work, the intrinsic hydration capacity is considered for the initial characterization of potential nonfouling functional groups, before surface functionalization makes hydration evaluation difficult. The objective of this work is to develop a simple method for evaluating the intrinsic hydration capacity of chemical groups and functional moieties to aide in the development of new nonfouling materials. The hydration ability of a chemical structure of interest can be estimated from the partial molal volume at infinite dilution. At infinite dilution, the solute-solute interactions are minimized and the solute-solvent interactions dominate the solution behavior.22 Thus, the partial molal volume at infinite dilution will only include the solute molecule and its hydrating solvent molecules. This infinite dilution behavior can be used to evaluate the intrinsic hydration capacity of the solute. The hydration volume and number of hydrating solvent molecules can be estimated by comparing the partial molal volume at infinite dilution to the solute van der Waals occupied volume. The hydration volume of chemical groups known to resist protein adsorption, like oligo(ethylene glycol), can be used to establish a critical hydration specification, or threshold value, for new nonfouling candidates. Experimental Materials and Methods Materials. Three classes of solutes were studied in this work: ethylene glycols, sugar alcohols, and glycine analogues. Oli-
10.1021/jp8065713 CCC: $40.75 2009 American Chemical Society Published on Web 12/11/2008
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go(ethylene glycol) containing four ethylene glycol repeat units (OEG4) was selected as a positive control because of its known nonfouling properties. The stereoisomeric sugar alcohols, mannitol (MAN) and sorbitol (SORB), were selected to probe hydrogen bond-driven hydration and to analyze any stereochemical effects. Furthermore, these molecules have also been shown to have nonfouling properties.4,18 The glycine analogues studied include the primary amine glycine (GLY), secondary amine sarcosine (1MG), tertiary amine dimethylglycine (DMG), and the quartenary amine trimethylglycine (TMG). The glycine analogues differ in their degree of methylation of the amine group and also range from neutral to zwitterionic. All of these solutes were purchased from Sigma-Aldrich and have a purity of g98%. Experimental Methods. Dilute aqueous solutions of each solute in 18.2 MΩ · cm water were prepared to specific measured molal concentrations using a balance with an accuracy of 1 × 10-5 g. The solutions were allowed to equilibrate at 20 °C before density measurements. The solution density was measured with a vibrating tube digital density meter (Mettler Paar DMA 45) with an established accuracy of 1 × 10-4 g/cm3. The solution density and molal concentration were used to calculate the apparent molal volume as follows:
φV )
103(d0 - d) M + d mdd0
(1)
where M is the solute molecular weight, m is the solution molal concentration, and d and d0 are the solution and solvent densities, respectively.23 φV is the apparent molal volume of the solute in the solution. When extrapolated to a zero solute concentration limit, the partial molal volume at infinite dilution, φV0 , can be obtained, and this quantity describes the solute-solvent interactions. In general, the interactions between water and a solute with a high hydration capacity led to an increase in the density resulting from the strong solute-solvent attractions. Because the molal volume is known to vary linearly with dilute solution concentration, the y-intercept in a plot of solute molality versus molal volume represents the partial molal volume at infinite dilution. Finally, the difference between the neat solute molecular volume, calculated as the van der Waals molecular volume, VvdW, and the partial molal volume at infinite dilution allows for the estimation of the number of bound water molecules.24 The van der Waals molecular volume was calculated in this work using Accelrys MS Modeling version 3.2, a commercially available molecular simulation tool. The molecules were built and equilibrated for 500 000 simulation steps before the molecular volume was calculated. In this analysis, a more hydrated solute will have a larger partial molal volume at infinite dilution than a less hydrated solute of similar molecular weight. This difference results from the space occupied by bound hydration water molecules. It can be difficult to experimentally measure interactions between individual solutes and hydrating water molecules. Molecular simulations can provide atomic-level descriptions of the solute-water interactions and structure. In this work, constant pressure and temperature (NPT) molecular dynamics (MD) simulations were used to validate the hydration estimates obtained from the partial molal volume experimental method. The commercially available simulation program CHARMM25 was used to construct each solute used in the volume experiments and run the dynamic simulations. However, the solute residue topological descriptions and connectivity were added
Figure 1. Solution molal volume as a function of solute molality. The data are presented as the mean of three separate measurements, and the error bars represent the standard deviation of these measurements.
to the CHARMM topology file. The partial atomic charges were calculated with the Rappe-Goddard charge equilibrium method.26 Each solute was built and then solvated in a preequilibrated water box. The final system was energy minimized to remove bad contacts and then heated to 300 K before 2.3 ns of MD simulations. The last 100 ps was used to evaluate the solute hydration by integrating the water-solute pair correlation function. The simulation box was subject to periodic boundary conditions in all three dimensions. The solvation box was constructed such that the half-box edge distance was always greater than the nonbonded cutoff distance. This precaution ensures no interactions between solute molecules or images were considered, thereby replicating the infinite dilution limit also used in the experimental study. The simulations were conducted with 1 fs time step in the canonical NPT ensemble. The temperature, set to 300 K, was controlled with the Nose-Hoover algorithm, and the pressure was held constant at 1 atm with pistonlike control of the simulation box dimension. The short-range van der Waals interactions were calculated by the potential switch method with a twin cutoff between 13 and 15 Å. The long-range electrostatic interactions were modeled with the force shift function at a cutoff of 15 Å. All simulation methods and algorithms used were implementations of the CHARMM program options. The CHARMM force field, version 27, was used for all solute atoms27 while the solvation water was modeled with the TIP3P force field.28 Results and Discussion In this work, the partial molal volumes of candidate nonfouling functional moieties were calculated from the measured density and concentration of aqueous solutions containing these solutes. From the partial molal volume data, the molecular volume at infinite dilution in the aqueous environment was calculated in order to compare the innate hydration capacity of the nonfouling group analogues. Figure 1 shows the calculated apparent molal volume based on the measured solution density for each of the nonfouling solutes studied. As expected, the apparent molal volume varies linearly with solution concentration. By extrapolating the linear fit to a concentration of zero, the partial molal volume at infinite dilution, φV0 , can be determined as the y-axis intercept. Table 1 presents the extrapolated partial molal volume at infinite dilution, φ0V, as well as the calculated van der Waals molecular volume, VvdW, for each solute studied. The error in φV0 was calculated based on standard linear regression error estimation methods as described
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TABLE 1: Summary of Volume Estimates for Tested Moieties solute
vdW volume (mL/mol)
φV0 (mL/mol)
φV0 (mL/mol) prev pub
OEG MAN SORB TMG DMG 1MG GLY
119.6 96.6 96.3 72.1 62.3 54.3 41.1
170.3 ( 3.1 133.2 ( 1.4 137.4 ( 1.3 90.8 ( 1.4 65.8 ( 1.1 59.0 ( 0.6 42.6 ( 0.4
166.3123
43.1930
TABLE 2: Total Number of Hydration Water Molecules for Tested Moieties solute
hydrating water (no. of molecules)
OEG MAN SORB TMG DMG 1MG GLY
4.33 3.24 3.51 3.17 1.25 1.18 1.05
Figure 2. Normalized solute hydration values for various chemical functional groups. The dashed line represents a threshold hydration capacity for high nonfouling performance.
in Taylor’s book.29 Our measurements and calculated volumes correspond well with other published values, when similar data were available.23,30,31 The solute molal volume is primarily influenced by the initial size and molecular weight of the solute, as larger solutes will have larger molal volumes. For all of the functional moieties examined, φV0 was larger than VvdW. φV0 indicates the volume of the moiety and its associated hydrating water molecules, while VvdW includes only the solute molecule itself, without environmental influences. Therefore, the difference between φ0V and VvdW is directly proportional to the number of water molecules associated with the solute. The number of hydrating water molecules is estimated by comparing the molecular volume of water to the difference between the two solute molecular volumes as follows:
Nwater
φV0 - VvdW,solute ) VvdW,water
(2)
The estimations of the number of hydrating water molecules for the moieties tested in this work are summarized in Table 2. Similar methods have been proposed that are based on calculated molecular surface area.24,32 The number of hydrating water molecules has previously been estimated with a space-filling method that counts how many water molecules could fit around a solute molecule. Those methods are based only on geometry and do not reflect any measurements of the solute-solvent interaction. By using the difference between the calculated molecular volume and the experimentally observed volume, our method can better estimate the actual number of hydration water molecules, not just the geometrically possible number of hydration water molecules. The number of hydrating water molecules interacting with each solute provides an approximation of the hydration capacity of the solutes studied. It is hypothesized that when a highly hydrated solute is attached to a surface with appropriate packing densities, it will generate a strong surface hydration layer. However, like the molal volume data, the number of hydration water molecules scales with the solute molecular size. The larger solute will always interact with more water molecules as there
is more solute available to the hydrating solvent. In order to account for the solute size and to more directly compare the hydration interaction between different solutes, the partial molal volume at infinite dilution was divided by the solute molecular weight to normalize the solute-solvent interaction. This normalized hydration value can be seen in Figure 2. When the solute experimental molecular volume is normalized by molecular weight, the resulting hydration trend correlates well with known nonfouling experimental results. Surfaces presenting OEG46 and TMG33-35 are both known to prevent nonspecific protein adsorption, and these two solutes have the largest two scaled molecular volumes (>0.7). MAN functionalized surfaces have also been shown to significantly limit protein adsorption, but not to the same extent as OEG4 or TMG.7 These experimental adsorption results correlate well with the scaled molecular volume data in which the hydration capacity of MAN is somewhat less than that of OEG4 and TMG but significantly greater than the other solutes. Molecular simulations have proposed that SORB functionalized surfaces should be as nonfouling as MAN functionalized surfaces, as the hydration value would indicate.18 However, corresponding experimental studies have not been conducted in comparable manners.4,7 In a structure-property survey of nonfouling surfaces conducted by Ostuni and colleagues, surfaces were functionalized with GLY and DMG analogues (entries 23 and 24), and they were found to adsorb significant amounts of protein after 30 min of exposure.4 This significant nonspecific adsorption correlates well with the lower scaled hydration value found in our experiments. Molecular simulations and spectroscopic studies of OEG4 suggest that the short oligomer has a helical structure. This helical structure creates an optimal spacing in the ether bond oxygen atoms that allows for hydrogen bonding, and water bridging, between the oxygen atoms, significantly increasing the hydration capacity of this solute.15,16,36-38 TMG is a zwitterionic molecule that contains both positively and negatively charged groups. The hydrating water molecules are bound to TMG via hydrogen bonding and through an ion solvation mechanism. The zwitterionic nature of this molecule allows for the hydration of the methylated nitrogen atom. High solvation is not favorable in the neutral DMG and 1MG systems due to the lack of a charged nitrogen group that can overcome the poor alkane-like solvation of the methyl groups. With only limited hydrogen bonding possible, GLY, DMG, and 1MG all interact weakly with water, creating a low intrinsic hydration capacity. The sugar alcohols, MAN and SORB, only interact with water through hydrogen bonding. While there are six hydroxyl groups available for hydrogen bonding, these results suggest that there
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Figure 3. Size-normalized hydration capacity of solutes obtained from both experiments and simulations. The number of hydrating water molecules is normalized by the solute molecular weight. The experimental volume is based on the calculated number of water molecules from Table 1. The simulation results are obtained by integrating the first peak of the solute-water pair correlation function. The dashed line represents a threshold intrinsic hydration capacity for nonfouling surfaces.
are only three hydrating water molecules per sugar alcohol solute. This is likely due to the relative proximity of the hydroxyl groups in the MAN and SORB structures. The pendant OH may be oriented such that one water molecule can interact with two solute OH groups, preventing further hydration. Constant pressure and temperature molecular dynamics simulations were used to validate the experimentally measured hydration capacity of the solutes studied. One solute molecule was placed in a water box to replicate the infinite dilution experimental condition. The water-solute pair correlation function,39,40 g(r), was used to calculate the number of water molecules associated with each solute. As in the experimental case, the number of hydrating water molecules obtained from the simulation scaled directly with solute size. The larger solutes, OEG4 and the sugars, interacted with more water molecules than the glycine analogues. Therefore, the number of hydrating water molecules was normalized by the solute molecular weight. If the solute molecular weight is proportional to R3 and the available surface area is proportional to R2, then the number of hydrating water molecules is proportional to the two-thirds power of the molecular weight, Mw2/3. Nevertheless, the normalization by Mw and Mw2/3 yields the same trend. Since the grooves associated with small molecules provide extra surface area, normalization by Mw is reasonable and straightforward. Figure 3 plots the normalized number of hydrating water molecules calculated from both experiments and simulation results. The intrinsic hydration capacity trends from both experimental measurements and simulation calculations are nearly identical. The exact values are different as the experimental and simulation methods evaluate the hydration capacity based on different parameters, the measured φV0 , and the calculated number of water molecules. By comparing our scaled hydration capacity, presented in Figure 3, with known protein adsorption experiments, it is possible to develop a critical hydration parameter for new nonfouling materials. The solute analogues of known nonfouling surface coatings, OEG, MAN, SORB, and TMG, all have scaled number of associated water molecules greater than 0.15. At the same time, the scaled molecular hydration capacities for DMG and GLY, both known to allow nonspecific protein adsorption, are significantly less. Our findings suggest a critical hydration capacity specification that when combined with appropriate
surface packing density and chain flexibility may lead to a nonfouling surface coating. To date, the number of chemical functional groups studied is too small to finalize a critical scaled molecular hydration volume, or number of associated water molecules, required to prevent protein adsorption, but the current results suggest that this value must be greater than 0.15. Furthermore, on the basis of this work, it is reasonable to propose our partial molal volume and NPT MD approach to evaluate solute hydration and help predict surface nonfouling ability. Conclusions The objective of this work was to develop a simple method to evaluate the intrinsic hydration capacity of molecules of interest for creating nonfouling surface coatings. Our results show that when the experimentally measured partial molal volume at infinite dilution is normalized by the solute molecular weight, the resulting scaled molecular volume correlates strongly with the ability of the solute to form surface coatings that resist nonspecific protein adsorption. Furthermore, the experimentally observed hydration capacity was validated by NPT MD simulations that show a similar trend in hydration capacity when the number of solute-associated water molecules is again normalized by the solute molecular weight. Chemical groups known to resist protein adsorption to surfaces, like OEG4, MAN, and TMG, have scaled molecular volumes and normalized number of associated water molecules significantly greater than other chemical groups, like GLY and DMG, which do not resist protein adsorption. Nonspecific protein adsorption can be prevented with surface coatings that combine high intrinsic hydration capacity with appropriate surface flexibility and packing density. Both the molar volume measurements and the NPT hydration simulations can evaluate the hydration capacity of solute groups regardless of the types of hydration interaction present, i.e., hydrogen bonding or ionic solvation. These simple hydration evaluation techniques allow for rapid screening to aide in novel nonfouling material development. Acknowledgment. This work was funded by the National Science Foundation (CBET0827274).
Hydration of “Nonfouling” Functional Groups References and Notes (1) Ratner, B. D.; Hoffman, A. S.; Schoen, F. J.; Lemons, J. E. Biomaterials Science: An Introduction to Materials in Medicine; Academic Press: San Diego, 1996. (2) Boozer, C.; Yu, Q. M.; Chen, S. F.; Lee, C. Y.; Homola, J.; Yee, S. S.; Jiang, S. Y. Sens. Actuators, B 2003, 90 (1-3), 22. (3) Horbett, T. A. In Biomaterials: Interfacial Phenomena and Applications; Peppas, S. L. C. a. N. A., Ed.; American Chemical Society: Washington, DC, 1982; Vol. 199, p 233. (4) Ostuni, E.; Chapman, R. G.; Holmlin, R. E.; Takayama, S.; Whitesides, G. M. Langmuir 2001, 17 (18), 5605. (5) Chapman, R. G.; Ostuni, E.; Takayama, S.; Holmlin, R. E.; Yan, L.; Whitesides, G. M. J. Am. Chem. Soc. 2000, 122 (34), 8303. (6) Li, L. Y.; Chen, S. F.; Zheng, J.; Ratner, B. D.; Jiang, S. Y. J. Phys. Chem. B 2005, 109 (7), 2934. (7) Luk, Y. Y.; Kato, M.; Mrksich, M. Langmuir 2000, 16 (24), 9604. (8) Ostuni, E.; Chapman, R. G.; Liang, M. N.; Meluleni, G.; Pier, G.; Ingber, D. E.; Whitesides, G. M. Langmuir 2001, 17 (20), 6336. (9) Shen, M. C.; Martinson, L.; Wagner, M. S.; Castner, D. G.; Ratner, B. D.; Horbett, T. A. J. Biomater. Sci., Polym. Ed. 2002, 13 (4), 367. (10) Jeon, S. I.; Lee, J. H.; Andrade, J. D.; Degennes, P. G. J. Colloid Interface Sci. 1991, 142 (1), 149. (11) McPherson, T.; Kidane, A.; Szleifer, I.; Park, K. Langmuir 1998, 14 (1), 176. (12) Pertsin, A. J.; Grunze, M.; Garbuzova, I. A. J. Phys. Chem. B 1998, 102 (25), 4918. (13) Tasaki, K. J. Am. Chem. Soc. 1996, 118 (35), 8459. (14) Li, L.; Chen, S.; Jiang, S. J. Biomater. Sci., Polym. Ed. 2007, 18 (11), 1415. (15) Zheng, J.; Li, L. Y.; Chen, S. F.; Jiang, S. Y. Langmuir 2004, 20 (20), 8931. (16) Zheng, J.; Li, L. Y.; Tsao, H. K.; Sheng, Y. J.; Chen, S. F.; Jiang, S. Y. Biophys. J. 2005, 89 (1), 158. (17) Besseling, N. A. M. Langmuir 1997, 13 (7), 2113. (18) Hower, J. C.; He, Y.; Bernards, M. T.; Jiang, S. Y. J. Chem. Phys. 2006, 125–21. (19) Vanderah, D. J.; La, H. L.; Naff, J.; Silin, V.; Rubinson, K. A. J. Am. Chem. Soc. 2004, 126 (42), 13639. (20) Morra, M. J. Biomater. Sci., Polym. Ed. 2000, 11 (6), 547. (21) Lark, B. S.; Patyar, P.; Banipal, T. S.; Kishore, N. J. Chem. Eng. Data 2004, 49 (3), 553.
J. Phys. Chem. B, Vol. 113, No. 1, 2009 201 (22) Koretsky, M. D. Engineering and Chemical Thermodynamics; Wiley: Hoboken, NJ, 2004. (23) Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. J. Solution Chem. 1978, 7 (6), 463. (24) Tirosh, O.; Barenholz, Y.; Katzhendler, J.; Priev, A. Biophys. J. 1998, 74 (3), 1371. (25) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4 (2), 187. (26) Rappe, A. K.; Goddard, W. A. J. Phys. Chem. 1991, 95 (8), 3358. (27) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; JosephMcCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E.; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102 (18), 3586. (28) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79 (2), 926. (29) Taylor, J. R. In An Introduction to Error Analysis: The study of uncertainties in physical measurements; University Science Books: Sausalito, CA, 1997; p 181. (30) Millero, F. J.; Surdo, A. L.; Shin, C. J. Phys. Chem. 1978, 82 (7), 784. (31) Yasuda, Y.; Tochio, N.; Sakurai, M.; Nitta, K. J. Chem. Eng. Data 1998, 43 (2), 205. (32) Chalikian, T. V.; Sarvazyan, A. P.; Plum, G. E.; Breslauer, K. J. Biochemistry 1994, 33 (9), 2394. (33) Chen, S. F.; Jiang, S. Y. AdV. Mater. 2008, 20 (2), 335. (34) Chen, S. F.; Yu, F. C.; Yu, Q. M.; He, Y.; Jiang, S. Y. Langmuir 2006, 22 (19), 8186. (35) Zhang, Z.; Chao, T.; Chen, S. F.; Jiang, S. Y. Langmuir 2006, 22 (24), 10072. (36) Smith, G. D.; Jaffe, R. L.; Yoon, D. Y. J. Phys. Chem. 1993, 97 (49), 12752. (37) Wang, R. L. C.; Kreuzer, H. J.; Grunze, M. J. Phys. Chem. B 1997, 101 (47), 9767. (38) Wang, R. L. C.; Kreuzer, H. J.; Grunze, M. Phys. Chem. Chem. Phys. 2000, 2 (16), 3613. (39) Allen, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (40) Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide; Springer: New York, 2002.
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