Langmuir 2007, 23, 5439-5444
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Atomistic Simulations to Compute Surface Properties of Poly(N-vinyl-2-pyrrolidone) (PVP) and Blends of PVP/Chitosan† B. Prathab and Tejraj M. Aminabhavi* Molecular Modeling DiVision, Center of Excellence in Polymer Science, Karnatak UniVersity, Dharwad, India 580 003 ReceiVed NoVember 4, 2006. In Final Form: February 14, 2007 Atomistic simulations were performed on poly(N-vinyl-2-pyrrolidone) (PVP) and its blends with chitosan (CS) in different ratios using molecular mechanics (MM) and molecular dynamics (MD) simulations in three-dimensionally periodic and effective two-dimensionally periodic condensed phases. Four independent microstructures were generated to analyze their surface properties. The calculated surface-energy values for PVP compared quite well with the experimental data reported in the literature. The density profile was analyzed, and the structure of the films showed an interior region of the bulk density. Various components of the energetic interactions (torsional, van der Waals, etc.) were examined to gain deeper insight into the nature of regular and anomalous interactions between the bulk and the surface films. Surface energies of PVP/CS blends were computed by MD simulations using the bulk pressurevolume-temperature (PVT) parameters. Bulk properties such as the cohesive energy density (CED) and solubility parameter (δ) were calculated using MM and MD simulations in the NVT ensemble under periodic boundary conditions. The Flory equation of state was used to compute the thermal expansion coefficient as well as PVT parameters. These surface-energy values agreed well with the surface-energy data calculated using the Zisman equation, which were also in accordance with the experimental observations. The results from this study suggest that computer simulations would provide valuable information on polymers and polymer-blend surfaces.
1. Introduction Surface properties of polymers are extremely important in many practical applications that manipulate wetting, friction, and wear-resistance characteristics of a surface.1 In this regard, the dominant role played by polymeric surfaces and their characterization has triggered active research interest in fundamental understanding of surface properties using well-established polymer theories and computer simulations. To understand the compatibility of two different homopolymers, their surface properties in addition to chemical/physical interactions as well as mechanical strengths are extremely important. Therefore, prediction of polymer surfaces in terms of surface parameters has a fundamental value in designing high-performance polymers that are required in innumerable engineering applications including coatings, adhesives, and biomaterials.2-4 However, for a deeper understanding of polymer surfaces and related phenomena, computer simulation protocols have been proven to be quite efficient, and hence efforts have been made to explore the local structure and properties in the interfacial region, particularly when experimental evidence on macromolecular organization at surfaces is scarce. In recent years, because of increased growth in computing power at relatively low prices and advances made in the application of statistical mechanical tools to study polymer chain dynamics, it has become possible to employ atomistic simulation protocols effectively to elucidate the surface phenomena of † This article is Center of Excellence in Polymer Science communication no. 162. * Corresponding author. E-mail:
[email protected]. Fax: 91-8362771275.
(1) Anton, D. AdV. Mater. 1998, 10, 1198. (2) Feast, W. J.; Munro, H. S. Polymer Surfaces and Interfaces; Wiley: New York, 1987. (3) Price, G. J.; Ashok Kumar, M.; Grieser, F. J. Phys. Chem. B 2003, 107, 14124. (4) Zisman, W. A. Contact Angle, Wettability, and Adhesion; Advances in Chemistry Series 43; American Chemical Society: Washington, DC, 1964.
polymers and thin films. Such an in-depth understanding of polymer surfaces at the molecular level offers the tremendous capability to modify polymer surfaces for various technological issues of adhesion, blends, lubrication, and biocompatibility. Simulation protocols are useful in accounting for specific peculiarities of the individual types of monomers in a long-chain polymer. In this sense, the recently developed atomistic simulation protocols are quite useful in studying polymer blends where differences in the surface properties of individual homopolymers that are critical in affecting the physiochemical properties of the system can be predicted accurately. In the past, various theoretical simulation methods have been devoted to the study of surface properties of a variety of polymers. The noteworthy contribution of Madden5 provided a study to utilize the lattice Monte Carlo simulation to understand the free surface of a polymer melt using an efficient pseudo-kinetic algorithm. In later years, there has been much interest in simulating polymer melts between solid surfaces. For instance, the work of Brinke et al.6 and Theodorou et al.7 utilized the lattice Monte Carlo simulations. Apart from these previous studies, a novel approach in studying the polymer films was developed to study the surface properties. In this respect, Mansfield and Theodorou8 studied the surface structural features and interfacial thermodynamic properties of glassy polymers through molecular mechanics (MM) and molecular dynamics (MD) simulations. This is indeed one of the first investigations of the free surfaces of amorphous polymers using MD simulation strategies. Intensive research activity on the utilization of MM and MD simulations has since been considered to be quite valuable in predicting the surface properties of polymers.9,10 (5) Madden, W. G. J. Chem. Phys. 1987, 87, 1405. (6) Ten, Brinke, G.; Ausserre, D.; Hadzioannou, G. J. Chem. Phys. 1988, 89, 4374. (7) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1989, 22, 3143. (8) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1990, 23, 4430. (9) Ijantkar, A. S.; Natarajan, U. Polymer 2004, 45, 1373.
10.1021/la063228u CCC: $37.00 © 2007 American Chemical Society Published on Web 04/03/2007
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Figure 1. Chemical structure of poly(N-vinyl-2-pyrrolidone) (PVP).
In the present research, we have employed MM and MD simulations to determine the surface energy of poly(N-vinyl2-pyrrolidone) (PVP), a well-known and widely used synthetic polymer having good biocompatibility that is used as a biomaterial or additive in drug delivery research;11,12 its structure is shown in Figure 1. PVP can be easily fabricated as a film from a solution casting method and has been widely used as a protective colloid, suspending agent, dye-receptive agent, binder, stabilizer, detoxicant, and complexing agent.13 Hydrogels formed from PVP have excellent transparency and biocompatibility, which prompted its use as the main component of temporary skin coverings and wound dressings. Blending of PVP was considered to be quite significant in developing blend hydrogels with a variety of other polymers that also have biomedical applications.14 The objective of this article is therefore to report comprehensive computational investigations to understand the PVP surface properties as well as PVP/chitosan blends utilizing the Flory equation of state model.
2. Modeling Details Simulations were performed using the MS modeling 3.1 software procured from Accelrys (San Diego, CA) as used in Pentium-based computers. MM and MD simulations have been performed using the DISCOVER package15 by employing the COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) force field.16,17 This force field has been widely used to optimize and predict the structural, conformational, and thermophysical condensed-phase properties of the polymers.18 Minimization was performed using the steepest descent approach followed by the conjugate gradient method with a convergence level of 0.01 kcal/mol/Å. The Discover molecular dynamics employing the Anderson thermostat1919 was used to control the temperature fluctuations. The velocity Verlet algorithm20 was used for the integration of equations of motion. The commonly encountered cutoffs21 were atom-based and groupbased. In the former case, the disadvantage is that the method is computationally expensive and hence was not found to be suitable for generating long-chain dynamics trajectories. However, the group-based approach was very efficient and yields substantially accurate results.22 The nonbonded interactions were (10) Prathab, B.; Aminabhavi, T. M.; Parathasarthi, R.; Manikandan, P.; Subramanian, V. Polymer 2006, 47, 6914. (11) Altemeier, W. Arch. Surg. 1954, 69, 309. (12) Hong, Y.; Chirila, T.; Vijaysekaran, S.; Shen, W.; Lou, X.; Dalton, P. J. Biomed. Mater. Res. 1998, 39, 650. (13) Barabas, E. S. In Concise Encyclopedia of Polymer Science and Engineering; Kroschwitz, J. I., Ed.; John Wiley: New York. 1990; p 1236. (14) Huglin, M. B.; Zakaria, M. B. J. Appl. Polym. Sci. 1986, 31, 457. (15) Lippa, K. A.; Sander, L. C.; Mountain, R. D. Anal. Chem. 2005, 26, 7852. (16) Sun, H. J. Phys. Chem. B 1998, 102, 7338. (17) Rigby, D.; Sun, H.; Eichinger, B. E. Polym. Int. 1997, 44, 311. (18) Prathab, B.; Parthasarathy, R.; Subramanian, V.; Aminabhavi, T. M. Theor. Chem. Acc. 2007, 17, 167. (19) Andersen, H. C. J. Chem. Phys. 1980, 72, 2384. (20) Verlet, L. Phys. ReV. 1967, 159, 98. (21) Brooks, C. L., III; Montgomery Pettitt, B.; Karplus, M. J. Chem. Phys. 1985, 83, 5897. (22) Eichinger, B. E.; Rigby, D.; Stein, J. Polymer 2002, 43, 599.
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calculated using the group-based method with explicit atom sums being calculated to 9.5 Å. 2.1. Amorphous Cell. In the present study, the PVP chain in its isotactic stereochemical structure was generated by selecting 50 monomer units. The chain was minimized, and the cubic bulk cell with an edge length of 20.7028 Å was constructed by packing a single chain into a box with periodic boundary conditions. The edge length of the periodic box was chosen on the basis of the experimental bulk density of PVP (1.04 g/cm3). The method employed in the amorphous cell module of the Material studio was the combined use of an algorithm developed by Theodorou and Suter23 and the scanning method of Meirovitch.24 The initial structures have very high potential energy as a result of nonbonded interactions between the atoms of a polymer chain, which arise from an overlap of atoms in the simulated initial structure. Also, at this stage of simulation, atoms of the polymer do not uniformly occupy the cubic unit cell. Therefore, the total energy of the initial structure should be minimized. The potential energy of the structure was minimized using the algorithms (steepest descent and conjugate gradient). The relaxation of high-energy structures followed a high-temperature molecular dynamics run performed at 500-1000 K for 10 ps to shake the cell out of the unfavorable local minima that had high energies. Subsequently, systems were equilibrated to 100 ps of dynamics at 300 K with the snapshots being saved every 0.1 ps during the last half of the run. The conformer with a minimum potential energy was selected and minimized to a convergence of 0.01 kcal/mol/Å. The size and shape of the cubic cells were kept constant during the MD runs. Cells having acceptable potential energies were selected, and a relaxation molecular dynamics simulation was performed at 300 K on short-listed samples for 300 ps. The final energy-minimized samples were used for all property calculations. These amorphous cells were subsequently used to generate the thin films. 2.2. Thin Films (Free Surfaces). Thin film generation and relaxation were performed according to the method described previously.25 In the present study, extending the z dimension of the 3D bulk periodic cell to 100 Å created the initial samples of amorphous thin films of PVP. The z direction specifies the direction perpendicular to the plane of the surface of the thin film. This cell extension resulted in two free surfaces per thin film. Relaxation of the initial structures formed by conversion from the bulk to the film surface was achieved by subjecting thin films to MM energy minimization followed by a high-temperature MD stage (500-1000 K). The relaxation procedure employed in this work was similar to the method described earlier for the bulk. Sufficient relaxation of the structures and acceptable fluctuations were observed for the potential energy in order to ascertain whether samples were suitable for the purpose of estimating the surface properties. The surface energy was calculated from the difference in energy between the thin film (Ethin film) and energy of the corresponding 3D bulk amorphous cell (Eamorphous cell) divided by the surface area created by the formation of the thin film given by
γ)
Ethin film - Eamorphous cell 2A
(1)
Here, the surface area is 2A because as two surfaces of area A were formed by the creation of a thin film. The total potential energy decomposition for the formation of thin films includes (23) Theodorou, D. N.; Suter, U. W. Macromolecules 1985, 18, 1467. (24) Meirovitch, H. J. J. Chem. Phys. 1983, 79, 502. (25) Natarajan, U.; Tanaka, G.; Mattice, W. L. J. Comput. Aided Mater. Des. 1997, 4, 193.
PVP and PVP/Chitosan Surface Properties
the bond length (stretch) and bond angles (bend), torsional potential (torsion), energy deviations due to out-of-plane inversion (oop), and cross terms to account for bond or angle distortions caused by the nearby atoms. Nonbonded interactions involve van der Waals (vdW) and electrostatic (Coulomb) energy terms. The contributions of these terms will be discussed in section 4.1.
3. Surface Energy of Blends Evaluating the surface energy of binary polymer blends would be important if the surface composition differed from the bulk composition. Dee and Sauer26 determined the surface tension of a series of low- and high-molecular-weight poly(dimethyl siloxane) (PDMS) blends and compared the experimentally obtained PVT data with Cahn-Hillard theory, where the FloryOrwill-Vrij equation of state27 was successfully used to model the surface properties of the blends. Kammer28 estimated the surface energy of miscible polymer blends of poly(vinyl methyl ether)/poly(styrene) using the well-known thermodynamic theory. Later, Kano and Akiyama29 estimated the surface energy of blends of poly(ethyl acrylate) and poly(vinylidene fluoride-co-hexafluoro acetone) experimentally using the contact angle method30 as well as bulk PVT properties.31 These methods were found to be very useful in estimating the surface energy of miscible binary blends. It may be noted that in the literature no effort has been made to employ molecular simulation tools to predict the surface energy of polymer blends. Hence, attempts to employ the MD simulation protocol techniques to calculate the surface energy of the chosen polymer blends are novel. As previously discussed,32 the surface properties of chitosan (CS) were determined from MD simulations. In the present investigation, blends of PVP and CS have been modeled to predict their surface properties. In recent years, blends of natural polymers with synthetic polymers have been used in many scientific disciplines, particularly as biomaterials, because these possess better physical properties and biocompatibility than do those of single components themselves.33-35 Chitosan and PVP do not normally exist as blends in nature, but specific properties of each of these polymers can be combined to produce blends that confer unique structural and surface properties. Chitosan as obtained by the deacetylation of chitin has a subunit of (1,4)-linked 2-amino2-deoxyb-D-glucan.36 Compared to other polysaccharides, CS has several inherent advantages such as biocompatibility, biodegradability, and low toxicity,37,38 which renders it to be useful in biomedical applications, including artificial skin, tissue regeneration, and drug delivery.39-41 3.1. Simulation Details. Oligomers with degrees of polymerization of 20 for PVP and 10 for CS have been selected in (26) Dee, G. T.; Sauer, B. B. Macromolecules 1993, 26, 2771. (27) Flory, P. J.; Orwoll, R. A.; Vrij, A. J. Am. Chem. Soc. 1964, 86, 3507. (28) Kammer, H. W. Polym. Networks Blends 1994, 4, 145. (29) Kano, Y.; Akiyama, S. Polymer 1996, 37, 4497. (30) Fox, H. W.; Zisman, W. A. J. Colloid Sci. 1950, 5, 514. (31) Patterson, D.; Rastogi, A. K. J. Phys. Chem. 1970, 74, 1067. (32) Prathab, B.; Aminabhavi, T. M. J. Polym. Sci., Part B: Polym. Phys., in press. (33) Giusti, P.; Lazzeri, L.; Petris, S.; Palla, M.; Gascona, M. G. Biomaterials 1994, 15, 1229. (34) Xiao, C.; Lu, Y.; Liu, H.; Zhang, L. J. Macromol. Sci. Pure Appl. Chem. 2000, A37, 1663. (35) Rao, K. P. J. Biomater. Sci.: Polym. Ed. 1995, 7, 623. (36) Park, S. B.; You, J. O.; Park, H. Y.; Haam, S. J.; Kim, W. S. Biomaterials 2001, 22, 323. (37) Hudson, S. M.; Smith, C. In Biopolymers from Renewable Resources; Kaplan, D. L., Ed.; Springer: Berlin, 1998. (38) Roberts, G. A. F. Chitin Chemistry; MacMillan Press Ltd.: London, 1992. (39) Lipatova, T. E.; Lipatov, Y. S. Macromol. Symp. 2000, 152, 139. (40) Seal, B. L.; Otero, T. C.; Panitch, A. Mater. Sci. Eng. 2001, R34, 147. (41) Felt, O.; Buri, P.; Gurny, R. Drug DeV. Ind. Pharm. 1998, 24, 979.
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simulating the blend systems. The concentration of blends during the simulation step was controlled by including different ratios of the number of chains of CS to the number of chains of PVP. The density of the blend system was estimated on the basis of pure-component densities and by assuming a volume additivity relationship for PVP (1.04 g/cm3) and CS (0.67 g/cm3). A snapshot of the blend ratio (3PVP/3CS) is shown in Figure 2. At first, the MD simulations of oligomers of the blends were performed at 300 K for a wide range of compositions. The amorphous cell construction strategy and minimization process followed the same strategy as described before. The construction of an amorphous cell of 3D periodicity followed the same tactic, but amorphous phases were checked for filling space regularly after the initial construction of the amorphous cell. If two component chains are not well “mixed” (sufficient intermolecular contacts) in the initial configuration, then they are discarded and a new one is attempted. Minimization was carried out using the same algorithm with a convergence level of 0.1 kcal/mol/Å. As mentioned before, configurations have been generated individually for each system and relaxed to compute the cohesive energy density (CED). MD simulations under constant temperature and density (NVT ensemble) were performed for each configuration using the Discover program. Systems built with 3D periodicity were equilibrated in the NVT ensemble at 300 K. Molecular dynamics run for 50 ps were then performed to remove the unfavorable local minima that had high energies. Subsequently, the systems were subjected to 250 ps of dynamics at 300 K with the trajectories being saved every 0.1 ps during the last half of the run to calculate the physical properties of interest. In the molecular simulations, the cohesive energy, Ecoh or more often CED, is defined as
CED )
Ecoh Vmol
(2)
The Hildebrand solubility parameter, δ, is defined as
δ)
( ) Ecoh Vmol
1/2
(3)
3.1.1. Surface-Energy Estimation by Bulk PVT Properties. The surface energy of the polymer was evaluated with the bulk PVT properties30,42 using the relationship
γ ) γ* γ˜
(4)
where γ* and γ˜ are characteristic and reduced surface energies, respectively. According to Patterson and Rastogi,42 γ* is related to equation of state parameters given by
γ* ) k1/3 P*2/3 T*1/3
(5)
where k is the Boltzmann constant and P* and T* are the characteristic parameters for pressure and temperature, respectively. According to Prigogine and Saraga,43 the equation for reduced surface energy is
γ˜ ) M V ˜ -5/3 -
[
]
˜ 1/3 - 0.5 V ˜ 1/3 - 1 V ln V ˜2 V ˜ 1/3 - 1
(6)
where γ˜ and V ˜ are reduced values of the surface energy and molar volume, respectively; M is the fractional decrease in the (42) Patterson, D.; Rastogi, A. K. J. Phys. Chem. 1970, 74, 1067. (43) Prigogine, I.; Saraga, L. J. Chem. Phys. 1952, 49, 399.
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Table 1. Components of Internal Energy (kcal/mol) of the Four Independent Bulk Structures and the Corresponding Thin Films with the Ensemble-Averaged Surface Energy (γ) Expressed in mJ/m2 γ ) 38.88 total bond angle torsion oop cross vdW Coulomb
γ ) 30.83
γ ) 37.63
γ ) 42.35
cell 1
film 1
cell 2
film 2
cell 3
film 3
cell 4
film 4
-2430.2 128.5 596.6 -282.1 2.56 -281.6 -304.7 -2289.5
-2382.4 117.8 579.2 -306.6 2.01 -300.6 -236.6 -2237.6
-2463.7 128.5 603.9 -302.1 2.56 -271.4 -307.7 -2317.5
-2425.8 114.6 583.1 -312.2 2.11 -281.6 -252 -2279.8
-2482.1 120.4 586.8 -290.4 2.74 -245.7 -301.6 -2354.3
-2435.8 116.6 557.6 -299.3 2.36 -258.9 -240.9 -2313.3
-2399.8 128.5 600.6 -282.1 2.96 -255.6 -309.7 -2284.5
-2347.7 109.8 589.2 -306.6 2.56 -267.6 -236.6 -2238.5
nearest neighbors of a cell due to migration from the bulk phase to the surface phase, and its value varies from 0.25 to 0.29 for a closely packed cubic lattice. In the present calculations, we have taken M ) 0.29 to compute PVT parameters using the Flory equation of state.27,44 The reduced volume was calculated from the thermal expansion coefficient, R, using the relationship
4 1 + ( )RT] [ 3 V ˜) (1 + RT)
3
(7)
The characteristic pressure, P*, is defined as the ratio */ν*, where * is the total interaction energy per mer and ν* is the close-packed mer volume. Thus, P* is a direct measure of the cohesiveness or strength of intermolecular interactions. Hence, P* is equal to CED in the close-packed state42,45,46 because CED ≡ ∆Evap/V ) */ν* ≡ P*. The characteristic temperature, T*, was calculated using
T* )
TV ˜ 4/3 V ˜ -1 1/3
(8)
The thermal expansion coefficient, R, was calculated from the slope of the specific volume, VSP, versus temperature plot. To compute the specific volume for bulk PVT parameters, MD simulations were performed on the blends of PVP and CS of different compositions at various temperatures below 300 K. The procedure to calculate the specific volume using constantpressure simulation (NPT ensemble) has been investigated by Fried et al.47 The NPT ensemble molecular dynamics simulation
was preceded by the constructed and minimized structures of PVP/CS blends. In our initial approach, the systems were equilibrated for 50 ps in the NPT ensemble at 300 K. Using the equilibrated systems as the starting structure for performing dynamics at the next temperature, the temperature of the cells was lowered stepwise (5 K) from 300 to 270 K. At each temperature, amorphous cells were subjected to 150 ps NPT dynamics to determine the specific volume.
4. Results and Discussions 4.1. Surface Energy of PVP. The surface properties of PVP polymer were determined using the free surface (thin film) method by applying the MD simulations, and four independent thin films were generated. The surface area, A, is 20.7028 Å.2 Calculated values of CED and δ are 422.16 J/cm3 and 10.04 ( 0.20 (cal/ cm3)1/2, respectively. Also, the calculated solubility parameter of PVP agreed closely with the experimental value48 of 11.06 (cal/cm3)1/2. In Table 1, details of the internal energy components in the bulk as well as in the PVP film are listed. The average surface energy from four independent sets of systems was found to be 37.42 mJ/m2 with a standard deviation of 4.83 mJ/m2. The nonbonded energy terms, including van der Waals and Columbic electrostatic interaction energy terms, contribute most to the formation of the free surface of PVP films. However, torsional, bending, and bond-stretching energies of the films were lower than those of the amorphous cells. Because the density of the
Figure 3. Density profile as a function of distance from the center of mass for PVP. Table 2. Calculated CED and Solubility Parameter (δ) of PVP-CS Blends number of chains per composition density dimensions CED δ unit cell (wt % CS) (g/cm3) (Å) (J/cm3) (cal/cm3)1/2
Figure 2. Snapshot of the PVP/CS blend with a ratio of 3:3.
5PVP/1CS 4PVP/2CS 3PVP/3CS 2PVP/4CS
16.67 33.33 50.0 66.67
0.9771 0.9179 0.8553 0.7924
27.867 27.991 28.171 28.377
234.63 189.33 176.83 161.91
7.48 ( 0.05 6.73 ( 0.07 6.50 ( 0.10 6.22 ( 0.19
PVP and PVP/Chitosan Surface Properties
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Figure 4. Specific volume vs temperature for the 3PVP/3CS blend. Table 3. Calculated Thermal Expansion Coefficients (r), Reduced Values of Volume (V ˜ ) and Surface Energy (γ˜ ), Characteristic Surface Energy (γ*), and Surface-Energy Values of PVP/CS Blends blend ratios of PVP/CS
R × 104 (K-1)a
V ˜
5:1 4:2 3:3 2:4
5.35 (0.996) 5.51 (0.999) 6.0 (1.000) 6.42 (0.996)
1.1444 1.1477 1.1580 1.1710
γ˜
γ* (mJ/m2)
PVT
0.1448 0.1429 0.1377 0.1318
213.21 183.59 172.54 160.30
30.87 26.24 23.76 21.13
b
surface energy (mJ/m2) linear fitc Zismand 30.34 27.07 23.93 20.92
27.51 23.88 22.83 21.54
a The thermal expansion coefficient was calculated using eq 10. The correlation coefficient, r2, for the line connecting specific volume data is given in parentheses. b See eq 4. c See eq 11. d See eq 12.
surface layer was lower than in the bulk, the surfaces of the films have a small steric hindrance from the surroundings and have lower bond, bending, and torsional energies than do the bulk structures. The surface-energy calculations suggest that simulation results compare very well with the experimentally derived surface energy49 of PVP, whose value is 38.7 mJ/m2. The mass density profile for a thin film gives an indication of whether the film is of sufficient thickness that the interior of the film is indistinguishable from the bulk. The density profile in the films as a function of the distance from the center of mass of the film is shown in Figure 3. Density was calculated by slicing the z axis (normal to the surface) with a thickness of 2 Å. The density profile was described by a hyperbolic tangent function50 of type
( )[
( )]
Fo z F(z) ) 1 - tanh 2 xi
4.2. Blends of PVP/Chitosan. The density, CED, and solubility parameter values for different compositions of the blend of PVP/ CS are given in Table 2. The surface energy calculated using the bulk PVT parameters involved the computation of the thermal expansion coefficient, which is determined from the plots of specific volume obtained from the NPT dynamics versus temperature over the range of temperatures (300, 295, 290, 285, 280, 275, and 270 K). The model plots of specific volume versus temperature for the composition of 3PVP/3CS is shown in Figure 4. In each case, the least-squares fit was used to draw the line through the data points. Then, the equation describing these lines was used to calculate the thermal expansion coefficient, R, given by
R) (9)
where Fo is the bulk density and xi is the width of the surface region (2 Å). As expected, the profiles near the surface are sigmoidal. However, the density in the interior of the film reached the bulk value (1.04 g/cm3). The density drops at a distance of 8 Å from the surface and the density profile of PVP showed excellent agreement with the density values of 3D bulk structures. (44) Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833. (45) Sanchez, I. C.; Lacombe, R. H. Macromolecules 1978, 11, 1145. (46) Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838. (47) Fried, J. R.; Ren, P. Comput. Theor. Polym. Sci. 1999, 9, 111. (48) Brandrup J.; Immergut E. H. Polymer Handbook, 2nd ed.; WileyInterscience: New York, 1975. (49) Sionkowska, A.; Wisniewski, M.; Skopinska, J.; Vicini, S.; Marsano, E. Polym. Degrad. Stab. 2005, 88, 261. (50) Kumar, S. K.; Russell, T. P.; Hariharan, A. Chem. Eng. Sci. 1994, 49, 2899.
1 dν ν dT P
( )
(10)
Computed values of R and PVT parameters involved in the calculation of the surface energy of the blends are given in Table 3. It is evident that an increase in the concentration of CS monomers in the blend decreased the surface-energy values. To establish the validity of the data obtained using eq 4, the surface energy is plotted as a function of volume fraction of CS in the bulk as shown in Figure 5. Using Origin 5.0 version software, the straight line obtained by the least-squares approximation at the 95% confidence limit with the correlation coefficient r2 value of 0.9959 is given by the empirical equation
γ ) -18.52(Φb) + 33.74
(11)
where Φb is the volume fraction of CS in the bulk. Because γ is proportional to Φb, it is justifiable that γ calculated with eq 11 expresses the mean γ value in the bulk. Also, surface energies calculated using eq 11 are given in Table 3, which show the
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5. Conclusions
Figure 5. Relationship between the surface energy estimated by eq 4 and the volume fraction of CS in PVP/CS blends.
concurrence with the surface-energy data calculated using PVT parameters from eq 4. Alternatively, the surface energy (γ) of PVP/CS blends was also estimated from the CED values using the empirical equation given by Zisman.4
γ ) 0.75(Ecoh)2/3
(12)
The surface energies calculated from eq 12 are given in Table 3. Furthermore, these values compared well with the surfaceenergy data obtained from eq 4. Such agreement between the surface energies calculated from the PVT parameters from eq 11 and the Zisman method suggests the reliability of the method employed to compute the surface energy of the PVP/CS blends. In addition, the surface-energy trends of the blends of PVP/CS are in accordance with the experimental observations.49,51 (51) Caykara, T.; Alaslan, A.; Eroglu, M. S.; Guven, O. Appl. Surf. Sci. 2006, 252, 7430.
Simulation protocols employed in this research provided good insight into the surface properties of PVP as well as blends of PVP/CS. The surface energy of PVP was calculated using thin film methodology by employing the MM and MD simulations using the NVT ensemble. The calculation of δ for PVP using the COMPASS force field approach compared well with the literature data, suggesting that the simulated structures are well equilibrated. Surface properties such as density variations across the thickness of the thin film bearing two free surfaces per film showed the appropriate trend, and the surface energy compared well with the experimental data. The dominant molecular energy contributions to the formation of surfaces are mostly from the van der Waals and Coulombic energy terms. MD simulations were performed on the blends of PVP/CS using the bulk PVT parameters. The thermal expansion coefficient was computed from the plots of specific volume versus temperature obtained from NPT dynamics. As expected, with an increase in the CS component of the blend, a decrease in the surface energy of the PVP/CS blends was observed. The relationship between γ obtained from the bulk PVT parameters and volume fraction of CS exhibited a straight-line trend, which established the reliability of the methodology employed. The present study reveals that molecular modeling and simulation approaches are quite useful in predicting the surface properties of PVP and PVP/CS blends. Simulation results obtained for poly(N-vinyl-2-pyrrolidone) and its blend with chitosan are attempted for the first time using MD simulations. Acknowledgment. We thank the University Grants Commission, New Delhi (grant no. F1-41/2001/CPP-II), for the financial support to establish the Molecular Modeling Division at the Center of Excellence in Polymer Science (CEPS). We also thank Mr. J. Gopinath, Senior Associate, M/s Cognizant Technology Solution India Pvt. Ltd, Chennai, India, for helpful discussions. LA063228U
