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Development of AMBER-compliant transferable force field parameters for polytetrafluoroethylene

  • Orhan Kaya EMAIL logo , Alparslan Oztekin and Edmund B. Webb
Published/Copyright: August 8, 2024
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Open Chemistry
From the journal Open Chemistry Volume 22 Issue 1

Abstract

New transferable parameters for polytetrafluoroethylene (PTFE) compatible with the Assisted Model Building with Energy Refinement (AMBER) force field were developed by including many conformational states to improve accuracy. The Austin–Frisch–Petersson functional with dispersion hybrid density functional theory, advantageous for treating dispersion, was used to obtain quantum mechanical reference data. The restrained electrostatic potential method was used to compute the partial charges. The bonds, angles, and dihedral parameters were obtained via Paramfit software fitted to quantum mechanical data. The optimization of van der Waals parameters was obtained in the condensed phase through molecular dynamics simulations and the simplex method. These parameters were transferred to various molecular weights of PTFE assembly systems to calculate the density, radial distribution functions, power spectrum, and specific heat capacity. The highest percent error in density was 1.4% for the modeled PTFE ensembles. The calculated vibrational spectrum peaks closely matched experimental peaks with a maximum wavenumber deviation of 19 cm⁻¹. The highest percent error to specific heat capacity was 5%. These results represent a significant improvement over pre-existing potentials in the literature and provide parameters that can be used to model PTFE in many existing simulation codes.

Keywords: polytetrafluoroethylene; AMBER force field; parameter optimization; molecular dynamics simulation; density functional theory

1 Introduction

Polytetrafluoroethylene (PTFE) has a variety of commercial uses, particularly in engineering and medicine. Engineering research and applications involving PTFE cover a wide range of fields, such as membrane distillation application [1], semiconductor industry [2], and enhanced coating [3]. PTFE also finds extensive applications in various medical fields, such as dental prostheses and devices [4], hydrophobic acrylic equiconvex intraocular lenses [5], drug delivery [6], and blood substitutes [7], among others. PTFE is preferred in many other nano research fields because it is hydrophobic, thermally stable, inert, and non-toxic; it has a low friction coefficient, dielectric coefficient, and high surface resistance [8]. In PTFE applications, we may encounter poorly understood molecular behavior, such as short-lived interaction and unstable intermediates, as well as transition states that are impossible to observe experimentally [8,9]. The molecular design of PTFE materials is essential to improve PTFE applications and understand behavior at the nano-scale.

The need for an accurate PTFE force field has prompted prior work by some research groups. PTFE force field parameters available in the literature are dedicated to solving challenging problems related to experiments and reproducing experimental and theoretical data with the highest degree of accuracy. However, they usually produce some shortcomings. Okada et al. [10] developed an all-atom PTFE model using a molecular dynamics (MD) calculation package GEMS/MD for the reference molecules of perfluoroalkanes, including n-C3F8, n-C4F10, and n-C6F14; they utilized the HF/6-31G ab initio method, omitting the electron correlation effect [11,12]. The charges were derived using experimental dipole moment data. The bond, angle, and dihedral parameters were derived using the first principles method. They optimized the van der Waals (vdW) parameters by adding artificial nonbonding potentials between atoms separated by four bonds at positions 1–5 (vdW1−5). They claimed that the “1−5” interactions involving long PTFE chains are significant because the attractive interactions between fluorine atoms at these positions can affect the molecule’s conformation and properties. However, articles published later showed that the PTFE chain helix, affected by the artificial vdW1−5 potential functions between an atom and its fourth bond partner, did not adequately describe the energy landscape. While the trans conformations (t+, t−) closely matched the theoretical calculation results, the energy plot generated using the force field parameters failed to reproduce gauche conformations (g+, g−).

Jang et al. [13] developed a new Dreiding-type valence potential set for analyzing vdW1−5 non-bond interactions and predicted helical conformations. They conducted B3LYP\6-31G* [14,15] model chemistry employing the Hessian-biased singular-value decomposition technique [16] to derive bonds, angles, torsional, and molecular vibrational frequency parameters with Dreiding functional form by including many effects of electron correlation except treatment of dispersion. The charges were derived with Mulliken population atomic point charges [17]. They compared energy-minimized conformations between reference data and the force field of longer per-fluorinated alkanes. The authors concluded that Coulomb repulsion is the dominant helicity source for the all-trans conformations. They predicted the correct helical minima with t+, t−, and helical (h+, h−) conformations. However, at the onset of bending torsional angle values, the g+ and g− conformational sets proved unstable.

Watkins and Jorgensen [18] proposed another all-atom parameter set for PTFE molecules. They derived the force field for PTFE using OPLS functional form; their quantum mechanical data were generated using the LMP2/cc-pVTZ(−f) [12,19] and HF/6-31G* [11,12] theoretical method that adds corrections to achieve superior accuracy for electron correlation without treatment of dispersion. Despite good predictions of densities and heat of vaporization, Borodin et al. [20] showed that the transferability of the n-C4F10 and n-C5F12 could not adequately define conformational energetics by using the same torsional parameters. Thus, Borodin et al. derived bonds, angles, and nonbonded parameters using MP2/aug-cc-pvDz [12,21] and B3LYP/D95+* [12,14] model chemistry. They provided a satisfactory description of the transferability for n-C4F10 and n-C5F12 but exhibited notably less precise thermodynamic data, encompassing density and heat of vaporization.

The general AMBER force field (GAFF) [22] database contains parameters for numerous polymers, including PTFE. Bhowmik et al. [23] concluded that the standard GAFF necessitates parameter tuning to precisely predict specific heat across various polymers, PTFE included.

Consequently, providing a comprehensive description of PTFE solely based on force field parameters proves challenging. As indicated above, various studies have created new force field parameters. Still, they faced difficulties representing all conformational states, achieving transferability accuracy, obtaining precise thermodynamics (density, heat of vaporization), and generating more reliable charge parameters. To overcome inconsistencies in PTFE parameterizations in the literature, we developed Assisted Model Building with Energy Refinement (AMBER)-compliant transferable force field parameters for PTFE by carrying out the advanced APFD\6-31G* [12,24] model chemistry to characterize a large set of conformational states. The Austin–Frisch–Petersson functional with dispersion (APFD) hybrid density functional theory method involving the dispersion process is susceptible to the integration grid and generally requires finer grids than other functionals to achieve reasonable numerical stability [9]. Including electron correlation effects and considering both core and valence electrons contribute to more reliable and superior performance for a range of compounds than B3LYP [25,26]. The atomic partial charges were obtained through the restrained electrostatic potential (RESP) method [27] using Gaussian 16 version [28] and Antechamber software [29] packages. The paramfit program [30] was utilized for deriving bond, angle, and dihedral parameters to fit quantum mechanical reference data of 29 conformational sets of n-C4F10 reference molecules. The vdW interactions were optimized based on condensed phase heat of vaporization and density values. Using the force field parameters, MD simulations were conducted using a system of 50 reference molecules of n-C4F10. The findings demonstrated that the experimental values of density and heat of vaporization were accurately reproduced. Then, the force field parameters were transferred to simulate different molecular weights of PTFE to calculate density, power spectrum, and specific heat capacity. The potential advanced here demonstrates very good agreement with experimental measurements [31,32,33,34], and it shows notable improvement in the accuracy of its predictions compared to pre-existing interatomic potentials for PTFE reported in the literature [10,13,18,20,22].

2 Parameterization methods

2.1 AMBER interaction model

The AMBER interaction model, presented below, describes the potential energy of a molecular system [22].

(1) E = ∑ bond K r ( r − r eq ) 2 + ∑ angle K θ ( θ − θ eq ) 2 + ∑ torsion v n 2 [ 1 + cos ( n φ − γ ) ] + ∑ nonbond i < j ε ij σ ij r ij 12 − 2 σ ij r ij 6 + ∑ nonbond i < j q i q j r ij .

K r , K θ , and v n represent the force constants for the bonded terms. r eq is the equilibrium bond length; θ eq is the equilibrium bond angle. n is the multiplicity of the associated torsion angle, γ is the phase angle, and φ is the equilibrium torsion angle. ε ij is the energy well depth of the vdW interaction, r ij is the distance between nonbonded atoms i and j, and σ ij is the distance parameter of the Lennard–Jones (LJ) 12-6 function. In the final nonbonding term, q i and q j represent atomic charges.

In brief, the parameterization was performed using the following procedure: preliminarily, the atom types and the n-C4F10 reference molecule were modeled in .pdb format files using the Avogadro Molecular Editor [35]. Then, the parameter file for the force field was prepared, including all parameters to be fitted. The conformational sets were generated using Gaussian 16 [28] by specifying which dihedral angle to scan while relaxing other coordinates from an optimized n-C4F10 reference molecule; it was ensured that conformations spanned a considerable range in energy, including a few at high energy (Figure 3a). The paramfit tool was employed to fit all of the parameters in the conformational sets of bonded terms. Then, the LJ potentials were optimized using experimental data of the n-C4F10 reference molecule. Details about each of these steps are provided in the following sections. The quality of the parameter set was thoroughly examined and evaluated to ensure reasonable accuracy was obtained for all generated structures across the sampled conformational space.

2.2 Charge optimization

The atomic partial charges were obtained from QM wave functions and fitted to electron density and potential. Gaussian 16 was utilized to generate the electron density and electrostatic potential (ESP) at various points around the structure of isolated n-C4F10 molecules at the APFD\6-31G* level model chemistry and the corresponding optimized structure was directed to Antechamber to produce charges. The APFD\6-31G* method was chosen because it provides more reliable and superior performance for a range of compounds than B3LYP [25,26].

2.3 Bond, angle, and dihedral optimization

The Paramfit program [36] was utilized to derive force field parameters for bonded interaction terms by employing the least-squares method to minimize discrepancies between the molecular mechanics (MM) calculation using the present force field and QM energies [37]. The sets of conformations formed by the n-C4F10 structure in Figure 1 have 13 bonds: 3 C–C bonds, 10 C–F bonds, and 3 atom types assigned. The C–C bonds exhibit symmetry, while C–F bonds fall into two different groups, one corresponding to two fluorines bonded to the central carbon (CF2) and the other corresponding to three fluorines bonded to the triple carbons (CF3) [38].

Figure 1 (a) The molecular structure of PTFE consists of long chains with repeating units of tetrafluoroethylene (n units), as indicated in parentheses. (b) A bond schematic of the reference molecule is to be parameterized.
Figure 1

(a) The molecular structure of PTFE consists of long chains with repeating units of tetrafluoroethylene (n units), as indicated in parentheses. (b) A bond schematic of the reference molecule is to be parameterized.

The 32 sets of trans and gauche conformations of the n-C4F10 structure were generated by sampling dihedral angles at 15° intervals. We performed relaxed sampling at each specified dihedral angle to obtain more precise potential energy profiles, permitting all other internal coordinates to relax. These angles, defined for the carbon atoms in the reference molecule, ranged from 0° to 180°. Next, calculations for single-point energy and energy gradients were conducted for these conformations using APFD\6-31G* level theory. The conformations that result in duplicate QM energies were identified. Only one representative conformation was retained for further analysis; the others were excluded. This reduced the set of 32 to 29 trans and gauche conformations. Twenty-nine conformations combined 377 data points for bonds, 696 for angles, and 783 for dihedrals. The data points were employed to fit the AMBER energies to the quantum energies. The following minimization equation was used:

(2) ∑ i = 1 N w i [ ( E MM ( i ) − E QM ( i ) ) 2 + K ] = 0 ,

where K represents the internal inconsistency between quantum and AMBER energies for the system, and N stands for the number of data points corresponding to bonds, angles, and dihedrals, respectively. w i is a weight set to 1 by default. The goal is to iteratively solve equation (2) while minimizing each value of K (i.e., K bonds, K angles, and K dihedrals). During each iteration of the minimization process, Paramfit optimized the objective functions with the combination of K bonds, K angles, and K dihedrals to determine K values for bonds, angles, and dihedrals, respectively, aiming to minimize potential energy errors across conformational sets compared to quantum reference data. Then, the determined K bonds, K angles, and K dihedrals values were used for the entire data sets for bonds, angles, and dihedrals to fit the force field parameters. These minimization steps quantified the fit quality of MM equilibrium bonds, angles, and dihedral values, enabling the force field to provide reliable predictions for all 29 conformational sets. The conformational energies computed from the MM force field were compared to QM reference values to measure the accuracy of the final bonded interaction parameter values. Additionally, all bond lengths, angles, and dihedral angles obtained from the MM force field were compared to their QM counterpart values. The average absolute deviation (AAD) was computed for all quantities or traits and compared:

(3) A AD = ∑ t = 1 N | Q M t − M M t ̅ | N .

The root-mean-square deviation (RMSD) was also calculated.

(4) RMSD = ∑ t = 1 N ( QM t − MM t ) 2 N .

Four pairs of AAD and RMSD values were computed, one pair each from the conformational energies, bond lengths, bond angles, and dihedral angles. In the two preceding equations, QM t is a quantum mechanics reference value for the given trait t, MM t is the corresponding molecular mechanics calculated value, and N denotes the total number of data points for each trait (N = 29 for conformation energies, 377 for bond lengths, 696 for bond angles, and 783 for dihedral angles).

2.4 vdW optimization

We employed a combination of MD simulations using the GROMACS simulation package [39] and a simplex fitting procedure to optimize the vdW parameters for the PTFE reference molecule in condensed phases. The optimization process utilized experimental data of liquid density as 1.6 g/cm3 [18,31], and heat of vaporization as 5.46 kcal/mol [18,31]; the former property is susceptible to vdW length parameters and the latter to the energy parameters. In all fluid simulations, cubic boxes with periodic boundary conditions were used, and each cell contained 50 reference molecules of n-C4F10. The dimensions of the cubic box were set to have cell sides measuring 25 Å, and then the cell and coordinates were compressed to give experimental density. Once the initial configurations of the 50 reference molecules of n-C4F10 to be simulated were established, the optimization of the vdW was performed using the following procedure.

The fitting process involves creating a simplex with N vertices in an n-dimensional parameter space. Each vertex is represented by a vector x i = (x i1, x i2,…, x in ), where i ranges from 1 to N. The six LJ force field parameters (ε F, σ F, ε CF2, σ CF2, ε CF3, σ CF3) for three atom types (F, CF2, and CF3) indicate, here, n = 6. In the six-dimensional parameter space, an initial simplex with seven vertices (Table 1) was formed using the Nelder–Mead algorithm [40]. Each parameter was bounded as (0, 5) for all vertices defined. These bounds also define the range within which the parameters can be adjusted during optimization.

Table 1

Initial simplex has seven vertices in the parameter space

Vertex 1: (ε F, σ F, ε CF2, σ CF2, ε CF3, σ CF3)
Vertex 2: (ε F + δ, σ F, ε CF2, σ CF2, ε CF3, σ CF3)
Vertex 3: (ε F, σ F + δ, ε CF2, σ CF2, ε CF3, σ CF3)
Vertex 4: (ε F, σ F, ε CF2 + δ, σ CF2, ε CF3, σ CF3)
Vertex 5: (ε F, σ F, ε CF2, σ CF2 + δ, ε CF3, σ CF3)
Vertex 6: (ε F, σ F, ε CF2, σ CF2, ε CF3 + δ, σ CF3)
Vertex 7: (ε F, σ F, ε CF2, σ CF2, ε CF3, σ CF3 + δ)

In Table 1, δ is a small perturbation from the initial values and is set to 0.1 in this study. The optimization process has the following steps: 1: The system energy was minimized employing the vertex 1 parameter set for 10,000 steps using the steepest descent algorithm, followed by 1 ns NVT (constant number of particles N, volume V, and temperature T = 273 K) simulation to equilibrate the system further. 2: The equilibrated system was subsequently run in a sequence of short (20 ps) NVT simulations to test whether thermodynamic properties converged. 3: This was followed by a final data production NVT simulation for 100 ps, during which heat of vaporization was computed every 20 ps to allow for time averaging. These three steps were performed for each vertex. 4: The objective function, shown in equation (5) from the study of Faller et al. [41], was used to quantify the discrepancy between computed and target values of the heat of vaporization for each vertex.

(5) f target ( { Vertex n } ) = w 1 − Δ H vap ( { Vertex n } ) Δ H vap , target  2 1 / 2 ,

where w is the weight factor (set equal to 1 throughout this process), Δ H vap , target is the experimental value of heat of vaporization, and Δ H vap  ( { Vertex n } ) is the heat of vaporization value obtained from the parameters at Vertex n .

The heat of vaporization was calculated from

(6) Δ H v = E i + RT ,

where E i represents the total internal energy of the system for the ith vertex, R is the gas constant, and T is the temperature. The process of simplex optimization is depicted schematically in Figure 2. The vertices except the vertex with the highest objective function value (the worst vertex) were modified based on their objective function values and using the reflection, expansion, contraction, and shrinking operations [40,41,42] described below; all six parameters in the vertices were adjusted simultaneously. The next step is a production stage to define new parameters for the vertices. These update operations continue the movement of the vertices in the parameter space until the convergence criterion ( f target ( { Vertex n } ) ≤ 0.01) is achieved. The simplex update procedures carried out in these operations are shown in Table 2. It is important to note that the system box, previously equilibrated with the old parameters at each production stage, is no longer equilibrated with the new parameters. Thus, the system box must be re-equilibrated using the newly obtained vertex parameter sets to achieve a stable configuration.

Figure 2 A schematic representation of the update mechanisms within the simplex optimization algorithm.
Figure 2

A schematic representation of the update mechanisms within the simplex optimization algorithm.

Table 2

Simplex update operations and their equations in the parameter space

Operations: Equations
Centroid (c j ): c j = (x 1j + x 2j + … + x {N−1}j )/(N–1)
Reflection (r j ): r j = c j + (c j –x wj )
Expansion (e j ): e j = γ × r j + (1–γ) × c j
Contraction (co j ): co j = β × x wj + (1–β) × c j
Shrinking (s ij ): s ij = δ × x bj + (1–δ) × x ij

The simplex update procedure is iterative; j in Table 2 refers to the iteration number. First, the centroid coordinates are calculated by averaging the coordinates of all vertices, except the worst vertex coordinates denoted as x w = (x w1, x w2, …, x w6). Here, we consider a simplex with N vertices in a six-dimensional parameter space; each vertex is represented by a vector x i = (x i1, x i2, …, x i6), where i ranges from 1 up to N, where N denotes the total number of vertices in the simplex. In the centroid coordinate equation illustrated in Table 2, the sum of the coordinate values for all vertices except the worst vertex (the highest objective function value) is divided by (N–1). Applying the equation to each coordinate j, we can compute the centroid coordinates as (c = (c 1, c 2…, c n )) for the simplex. Then, each operation continues with the reflection of the vertex with the highest objective value. For each coordinate j, the reflected coordinate r j can be computed using the equation in Table 2. Applying the equation to each coordinate j, we can compute the reflected point coordinates r = (r 1, r 2,…, rn) for the worst vertex. An expansion operation is performed if the reflected vertex has a lower objective function value (i.e., better). For each coordinate j, the expanded coordinate e j can be computed using the equation in Table 2. In this equation, γ represents the expansion coefficient, dictating the magnitude of the expansion. Typically, γ is chosen to be greater than 1 (the value is set to γ = 2 in this research) to move the expanded point further away from the centroid. Applying this equation to each coordinate j, we can compute the expanded point coordinates e = (e 1, e 2,…, e n ) based on the reflected point and centroid. If the expanded point (or vertex) does not improve significantly or has a higher objective function value than the second-worst vertex, the contraction operation was performed according to the equation in Table 2. In this equation, β is the contraction coefficient, which determines the extent of the contraction. Typically, β is chosen to be less than 1 (β = (±)0.5 in this research) to move the contracted point closer to the centroid. Applying this equation to each coordinate j, we can compute the contracted point coordinates c o = (c o1, c o2,…, c on ) based on the worst vertex and centroid. The shrinking operation is performed if none of the above operations result in a better vertex. To do this, we shrink all vertices of the simplex toward the best vertex (the vertex with the lowest objective function value). We consider the best vertex coordinates as x b = (x b1, x b2,…, x b6) and the coordinates of each vertex in the simplex as x i = (x i1, x i2,…, x i6). For each vertex i and coordinate j, the shrunk coordinate s ij can be computed using the equation in Table 2. In this equation, δ is the shrinking coefficient, which determines the extent of the shrinking; note that δ used in shrinking is distinct from δ in Table 1. Typically, δ is chosen to be less than 1 (we set it to δ = 0.015) to move the vertices closer to the best vertex. Applying this equation to every vertex i and coordinate j, we can determine the shrunk coordinates s ij for all the simplex vertices.

This optimization process involves iteratively updating the vertices of the simplex based on the objective function evaluations until the convergence criterion ( f target ( { Vertex n } ) ≤ 0.01) was achieved. Then, the final simplex vertex is determined by the coordinates of each parameter (ε and σ) for each atom type (F, CF2, CF3). The optimized force field parameters were extracted from the converged simplex. These parameters represent optimal values aimed at minimizing the discrepancy between the calculated and reference values of the heat of vaporization. Following the acquisition of vdW parameters, an NPT simulation lasting 200 ps reached equilibrium after 50 ps at a temperature of 273 K and a pressure of 1 bar. This simulation aimed to assess the density and heat of vaporization to validate the optimized parameters.

3 Parameterization outcomes

3.1 Charge parameters

We successfully determined the RESP charge parameters for the n-C4F10 reference molecule for the F, CF3, and CF2 atom types. The RESP charge fitting process involved two main steps: QM calculations and charge optimization. We used APFD\6-31G* QM calculations to generate the ESP. Then, we used the Antechamber program to reproduce the same potential at the MM level by fitting the MM ESP to the QM ESP to minimize the deviation between the computed and target ESP values. Antechamber subsequently generated a file containing the RESP charges for each atom in the n-C4F10 reference molecule, as shown in Table 3. The RESP charge parameters indicate that F in the n-C4F10 molecule is negatively charged with q = −0.11018. This result is consistent with the electronegativity of F [43]. On the other hand, C in CF3 groups are positively charged with q = 0.33040, while C in CF2 groups are also positively charged with q = 0.22050.

Table 3

Optimized charge parameters for PTFE

Charge Atom types q ( e − )
F F −0.11018
C CF3 0.33040
C CF2 0.22050

3.2 Bonds, angles, and dihedral parameters

Paramfit software minimizes the objective function, deriving MM bonds, angles, and dihedral parameters relative to QM reference data. The optimization iterations were performed until the best combination of K bonds, K angles, and K dihedrals were obtained (i.e., when the objective function provided the lowest potential energy error across all data compared to the previous one). The convergence criterion proposed in Paramfit was used to validate the quality of the entire data parameter set at the final target K values. Figure 3(a) compares the MM energies of the 29 conformational sets obtained with the QM energies. A good agreement exists between MM and QM results; a more significant discrepancy exists for a few conformations, but the overall matching was considered satisfactory. All the MM-calculated results of bond lengths, bond angles, and dihedral angles were generated using the final force field parameter set after minimizing the objective function for all sets of geometries. These results were then compared to their QM-derived counterpart values. The MM bond length values exhibited excellent agreement with the QM values, with all cases not exceeding 0.1 Å difference (Figure 3(b)). Similarly, for the bond angles in Figure 3(c), discrepancies between MM and QM results did not exceed π/20 radians. Furthermore, the MM dihedrals data sets in Figure 3(d) showed agreement within π/10 radians across all data and conformational sets compared to the quantum reference data.

Figure 3 (a) Comparison between MM-calculated results and QM conformational energies across 29 conformational sets is presented. The comparison of bond lengths (b), bond angles (c), and dihedral angles (d) between MM-calculated results and QM reference values is shown, along with the total number of data points (Data), RMSD, AAD, and maximum value differences (Max). The color bar to the right of the plots shows the relative density of the data points (%).
Figure 3

(a) Comparison between MM-calculated results and QM conformational energies across 29 conformational sets is presented. The comparison of bond lengths (b), bond angles (c), and dihedral angles (d) between MM-calculated results and QM reference values is shown, along with the total number of data points (Data), RMSD, AAD, and maximum value differences (Max). The color bar to the right of the plots shows the relative density of the data points (%).

Given the overall satisfactory agreement between MM and QM calculations across such a wide range of conformations, the final equilibrium bond length r eq and bond force constant K r , equilibrium angle θ eq and angle force constant K θ , dihedral barrier height v n , dihedral phase γ and periodicity n shown in Tables 4–6 were then calculated.

Table 4

Optimized bond parameters for PTFE

Bond K r ( kcal ( mol   Å 2 ) ) ‒ 1 r eq ( Å )
CF2–CF2 251.4064 1.5898
CF2–CF3 251.4064 1.5898
CF2–F 361.8779 1.3363
CF3–F 361.8779 1.3363
Table 5

Optimized angle parameters for PTFE

Angle K θ ( kcal / ( mol radian 2 ) ) θ eq ( ° )
CF2–CF2–CF2 85.7729 110.9681
F–CF3–F 99.9229 109.3269
CF2–CF3–F 69.8039 108.5623
CF3–CF2–F 69.8039 108.5623
CF2–CF2–F 69.8039 108.5623
CF2–CF2–CF3 85.7729 110.9681
F–CF2–F 99.9229 109.3269
Table 6

Optimized dihedral parameters for PTFE

Dihedral Divider v n ( kcal / mol ) γ n
CF2–CF2–CF2–CF2 1 −1.1301 0.0 −3.0
CF2–CF2–CF2–CF2 1 0.3810 0.0 −1.0
CF2–CF2–CF2–CF2 1 4.3339 180.0 2.0
CF2–CF2–CF2–CF3 1 −1.1301 0.0 −3.0
CF2–CF2–CF2–CF3 1 0.3810 0.0 −1.0
CF2–CF2–CF2–CF3 1 4.3339 180.0 2.0
CF2–CF2–CF2–F 1 −0.3651 0.0 −3.0
CF2–CF2–CF2–F 1 13.2574 0.0 −1.0
CF2–CF2–CF2–F 1 0.9940 180.0 2.0
CF2–CF2–CF3–F 1 −0.3651 0.0 −3.0
CF2–CF2–CF3–F 1 13.2574 0.0 −1.0
CF2–CF2–CF3–F 1 0.9940 180.0 2.0
CF3–CF2–CF2–F 1 −0.3651 0.0 −3.0
CF3–CF2–CF2–F 1 13.2574 0.0 −1.0
CF3–CF2–CF2–F 1 0.9940 180.0 2.0
F–CF2–CF2–F 1 0.0469 0.0 −3.0
F–CF2–CF2–F 1 18.2421 0.0 −1.0
F–CF2–CF2–F 1 1.1050 180.0 2.0
F–CF2–CF3–F 1 0.0469 0.0 −3.0
F–CF2–CF3–F 1 18.2421 0.0 −1.0
F–CF2–CF3–F 1 1.1050 180.0 2.0

The relative conformational energies of n-C4F10, ranging from 0° to 180° as shown in Figure 4, were compared using advanced QM APFD/6-31G* model chemistry, as well as with the force field developed in the present work, and those previously developed by other researchers. Our force field results are almost identical to those of QM calculations. The energy barrier differences (g ↔ o, o ↔ a) between QM and the new force field were minimal, suggesting a realistic representation of the conformational landscape. In addition, we have compared results from previously developed force field parameters with their QM-derived counterpart values in Table 7.

Figure 4 Torsional energy versus C–C–C–C dihedral angle for n-C4F10 (a) from QM APFD/6-31G* calculations (blue circles) and the new AMBER force field presented here (squares); both of those data sets are results of the present work, and they are compared to calculations using the Okada et al. force field (triangles) [10], the generalized perfluoroalkane OPLS-AA force field (black circles) [18], and the n-C4F10 specific OPLS force field (stars) [18]. Panel (b) shows the same two data sets produced in the present work, and compares them to calculations using the force fields from Jang et al. (stars) [13] and Borodin et al. (black circles) [20].
Figure 4

Torsional energy versus C–C–C–C dihedral angle for n-C4F10 (a) from QM APFD/6-31G* calculations (blue circles) and the new AMBER force field presented here (squares); both of those data sets are results of the present work, and they are compared to calculations using the Okada et al. force field (triangles) [10], the generalized perfluoroalkane OPLS-AA force field (black circles) [18], and the n-C4F10 specific OPLS force field (stars) [18]. Panel (b) shows the same two data sets produced in the present work, and compares them to calculations using the force fields from Jang et al. (stars) [13] and Borodin et al. (black circles) [20].

Table 7

Comparison of the relative conformational energy differences (kcal/mol) of gauche (g), ortho (o), anti (a), and trans (t) for C4F10 as a function of the C–C–C–C torsional angle, using various force fields and their QM-derived counterpart values, including those from the present work [a], Okada et al. [10], the n-C4F10 specific and generalized perfluoroalkane OPLS-AA force field [18], Jang et al. [13], and Borodin et al. [20]

Model chemistry (QM) & force fields (FF) ref. gauche g ↔ o ortho o ↔ a anti trans
QM → APFD/6-31G* [a] 0.44 1.24 0.91 2.14 0.00 0.41
FF → Present work [a] 0.46 1.21 0.84 2.18 0.00 0.40
QM → HF/6-31G [10] 0.76 2.25 2.05 2.45 0.00 0.14
FF → Okada et al. [10] 0.73 1.46 2.33 1.73 0.00 0.11
QM → HF/6-31G* [18] 0.80 2.10 1.90 2.40 0.00 0.10
FF → OPLS-AA (n-C4F10 specific) [18] 1.10 1.91 2.27 1.97 0.00 0.06
FF → OPLS-AA (generalized perfluoroalkane) [18] 1.31 2.91 3.17 1.35 0.00 0.16
QM → B3LYP/6-31G* [13] 0.50 1.42 1.17 2.06 0.00 0.39
FF → Jang et al. [13] 0.45 1.37 1.16 2.19 0.00 0.36
QM → MP2/aug-cc-pvDz [20] 1.18 1.95 1.55 1.92 0.00 0.11
FF → Borodin et al. [20] 1.32 2.02 1.42 1.68 0.00 0.25

ref.: reference number, gauche (g): gauche energy. g ↔ o- energy difference between gauche and ortho, ortho (o): ortho energy. o ↔ a: energy difference between ortho and anti, anti (a): anti-energy, trans (t): trans energy, a present work.

The energy plots for the trans conformation (t+) from Okada et al. [10] and the n-C4F10 specific and generalized perfluoroalkane OPLS-AA force field [18] agree with the QM results. However, both approaches failed to accurately reproduce the gauche conformations barrier (g+, g−). Okada et al.’s force field calculated higher energy for the gauche conformer (0.73 kcal/mol) and significantly higher energy differences, shown in Table 7, at the barriers for g ↔ o (0.79 kcal/mol) and o ↔ a (0.72 kcal/mol), indicating a less favorable description of the potential energy surface compared to other methods. Watkins and Jorgensen [18] extended HF/6-31G model chemistry to derive n-C4F10-specific force field parameters by including polarization functions (indicated by the asterisk “*”). They also used LMP2/cc-pVTZ(-f) model chemistry to derive generalized perfluoroalkane parameter sets. Their force field performance for n-C4F10 was better than that of Okada et al. regarding energy differences. However, both parameter sets failed to reproduce conformation barriers accurately, as shown in Figure 4(a).

Jang et al.’s [13] force field sets, determined using the Dreiding-type valence potential, provided a satisfactory description of the lower energy differences and barriers, with gauche at 0.45 kcal/mol and barriers (g ↔ o: 0.05 kcal/mol), suggesting good accuracy. However, they reported that the g+ and g− conformational sets were unstable at the onset of bending torsion angle values for longer PTFE chains. This raises doubts about the transferability of these parameters and their reproduction of macroscopic properties because the authors have not provided any information on whether the force field parameters can predict macroscopic properties. Borodin et al.’s [20] parameter sets also provided a good description of the g+, g−, and t+ conformations for n-C4F10, reproducing torsional energy compared to QM calculations. However, their thermodynamic data, including density and heat of vaporization, were less precise compared to the present work (see below).

3.3 vdW parameters

Optimized vdW interaction parameters are presented in Table 8.

Table 8

Optimized vdW parameters for PTFE

vdW ϵ ( kcal / mol ) σ ( nm )
F 2.8486 0.0634
CF3 3.1499 0.0838
CF2 3.2340 0.0781

After vdW parameters were optimized, we calculated the heat of vaporization using

(7) Δ H vap ( T , P ) = ⟨ H gas ( T , P ) ⟩ − ⟨ H liq ( T , P ) ⟩ + RT ,

where ⟨ H gas ( T , P ) ⟩ represents the average total energy of the system in the vapor phase, ⟨ H liq ( T , P ) ⟩ represents the average total energy of the system in the liquid phase, R denotes the ideal gas constant, and T is the absolute temperature. The total energy included contributions from bonded and nonbonded interactions and kinetic energy. NPT simulations were conducted at 200, 273, and 298 K with a pressure of 101.3 kPa to calculate the average total energy in both liquid and gas phases, with 50 molecules in the liquid phase and 1 in the gas phase. Our results for the heat of vaporization and density were compared with the experimental data and results from other force fields in Figure 5.

Figure 5 Variation of density (a) and heat of vaporization (b) with temperature for n-C4F10.
Figure 5

Variation of density (a) and heat of vaporization (b) with temperature for n-C4F10.

The density of n−C4F10, as presented in Figure 5(a) (in g/cm3), found at 273 K, is 1.591. This performs better than the parameter sets from Jang et al. (1.650) [13], Borodin et al. (1.569) [20], and OPLS-AA (1.581) [18] but is nearly identical to the experimental value of 1.592 reported in the study of Brown and Mears [31]. At another temperature point, 200 K, the density we obtained is 1.820, compared with the experimental density of 1.810 [31]. This is better than the value from Borodin et al. (1.785) [20]. Our result for the heat of vaporization (kcal/mol), as presented in Figure 5(b), is 5.450 at a temperature of 273 K. This value is in close agreement with the experimental value of 5.460, as in the study of Brown and Mears [31]. This level of accuracy signifies an improvement over the results obtained using the parameter sets reported by Okada et al. (5.540) [10] and Borodin et al. (5.920) [20], indicating that our methodology provides a more precise match to the heat of vaporization data. However, even though the density is improved, the calculated heat of vaporization value at 273 K is the same as that obtained using the OPLS-AA force field. At 200 and 298 K, we could not compare the values we calculated due to a lack of experimental and previous force field data.

4 Validation procedures

Validations described in this section involved executing MD simulations in NPT or NVT equilibrium ensembles. For all of these simulations, the time step used was 2.0 fs, and short-range interactions were computed using LJ potentials with a 10 Å cutoff, supplemented with a dispersion correction to account for contributions to energy and pressure from long-range interactions. Beyond this distance, interactions were either ignored or handled using long-range correction methods to reduce computational cost while maintaining accuracy. Additionally, nonbonded interactions between atoms connected by three bonds or fewer were not computed to further streamline the calculations. Arithmetic (for length parameters) and geometric (for energy parameters) averaging rules were used to calculate LJ interactions. The simulation utilized the particle mesh Ewald [44] method to handle electrostatic interactions, coupled with the Nose–Hoover thermostat [45,46] to maintain the desired temperature (unless specified otherwise, simulations below were at T = 300 K). The Parrinello–Rahman approach [47] to regulate pressure at 1 bar was used in NPT ensembles.

4.1 Density distribution

This validation aims to transfer the derived AMBER force field parameters to PTFE models with varying molecular weights to determine the average density distribution in specific regions of these models and compare them against experimental density data to evaluate the accuracy and reliability of the derived force field parameters. Therefore, the QuantumATK molecular simulation software [48] was first utilized with the Monte Carlo method using the OPLS Potential Builder tool [49] to create PTFE models in varying sizes: [CF3-(C2F4)20-CF3]20 (this chemical configuration describes a polymer made up of 20 repeating units of a (CF3-(C2F4)20-CF3) chain. Each chain consists of a CF3 group, followed by 20 repeating units of C2F4 (tetrafluoroethylene), and another CF3 group at the other end), [CF3-(C2F4)40-CF3]40, [CF3-(C2F4)50-CF3]50, and [CF3-(C2F4)100-CF3]100. Then, the Force-Capped MD technique implemented in the QuantumATK software [48] was selected to model PTFE, aiming to mitigate concerns regarding atom overlap or artificially closed atoms within the system. Once the models with variable weights were created, the ACPYPE [50], a Python 3 tool, was employed to convert the force field from AMBER to GROMACS topology files. Then, all MD simulations were executed using GROMACS [39] to obtain the densities and radial distribution function (RDF) from well-equilibrated GROMACS trajectories. To probe if density variations existed within each molecular weight ensemble, density was first computed by dividing each system into slabs along the z-direction. Density in each slab was computed as ρ = m/V, where ρ is the density, m is the total mass of the atoms in that slab, and V is the volume of the slab. The average density in different sub-regions of each ensemble was compared, and no systematic variations were detected. For each ensemble, slab density data were averaged to determine the final density for that molecular weight. These results were then compared with experimental data and previous simulations. Visualizations and results are presented in Figure 6 and Table 9, respectively.

Figure 6 The equilibrated cubic PTFE ensembles of varying size: (a) [CF3-(C2F4)20-CF3]20, (b) [CF3-(C2F4)40-CF3]40, (c) [CF3-(C2F4)50-CF3]50, and (d) [CF3-(C2F4)100-CF3]100.
Figure 6

The equilibrated cubic PTFE ensembles of varying size: (a) [CF3-(C2F4)20-CF3]20, (b) [CF3-(C2F4)40-CF3]40, (c) [CF3-(C2F4)50-CF3]50, and (d) [CF3-(C2F4)100-CF3]100.

Table 9

Comparison of our density values from MD simulations of various-sized PTFE ensembles, with MD simulations using Okada et al. [10] and GAFF force field parameters [22], with the experimental density at 300 K reported in the study of Nunes et al. [32]

Molecular weights [CF3-(C2F4)20-CF3]20 [CF3-(C2F4)40-CF3]40 [CF3-(C2F4)50-CF3]50 [CF3-(C2F4)100-CF3]100 Okada force field GAFF force field Experimental value
Density (kg/m3) 2,151 2,201 2,171 2,161 1,900 1,820 2,180
Percent error (%) 1.4 0.9 0.4 0.8 13 17 0

Bhowmik et al. [23] conducted MD simulations of PTFE using GAFF parameters [22] for five chain lengths and reported a predicted density of 1,820 kg/m3. Okada et al. [10] performed MD simulations on amorphous PTFE assemblies and observed a predicted 1,900 kg/m3 density. The percentage of errors reported by Bhowmik et al. and Okada et al. was significantly higher than that of the present study.

4.2 RDF

The pair-specific spherical atomic RDFs g CF ( r ) were calculated to determine the coordination of fluorine (F) atoms around carbon (C) atoms over a GROMACS trajectory using the VMD GUI Plugin [51]. The RDF is determined by measuring the distances between atoms or particles within specified groups. These distance data are then converted into a histogram, where the occurrences of particles at various distances are counted. To obtain the RDF, the counts in the histogram are divided by the average density. The mathematical expression for the RDF, g CF ( r ) , is as follows:

(8) g CF ( r ) = ρ CF ( r ) ρ C · ρ F · ( 4 π r 2 ) · Δ r .

g CF ( r ) characterizes the spatial arrangement of F atoms around C atoms in a given system. It represents the probability of encountering an F atom located at a specific distance “ r ” from a C atom, normalized based on the system’s average C and F atom density. The number density of F atoms around a C atom at distance “ r ” is denoted by ρ CF ( r ) , while ρ C and ρ F refer to the densities of C and F in the assembled system. The width of the spherical shell (bin size), denoted as Δ r , is used to accumulate atoms within a distance range from “ r ” to “ r + Δ r ,” and the surface area of this shell is given by 4 π r 2 . The RDF results depicted in Figure 7 show that the PTFE system’s atomic interactions and structural properties remain relatively consistent and do not significantly alter with changes in ensemble size and/or molecular weight. Si et al. [52] observed that the pure amorphous PTFE peaks appear around 2Θ = 18°, 33°, 37°, 49°, 56°, 67°, and 69° in X-ray diffraction experiments using Cu-Kα radiation. These peaks match those in the RDF at 4.94, 2.73, 2.42, 1.86, 1.65, 1.38, and 1.36 Å, respectively. These peak values were compared with the calculated ones shown in Figure 7.

Figure 7 Comparison of experimental RDF peak values with RDFs for equilibrated cubic PTFE ensembles of various sizes: [CF3-(C2F4)20-CF3]20.
Figure 7

Comparison of experimental RDF peak values with RDFs for equilibrated cubic PTFE ensembles of various sizes: [CF3-(C2F4)20-CF3]20.

4.3 Power spectrum

The power spectrum or velocity density of states (VDOS) is calculated using data from an MD simulation according to the study of Agarwal et al. [53] as follows:

(9) P ( ω ) = ∫ − ∞ + ∞ C ( t ) e i ω t d t ,

where C ( t ) is the normalized velocity autocorrelation function (VACF). The calculation of the C ( t ) is as follows:

(10) C ( t ) = ∑ i = 1 m v k ( i ) v k ( i + n ) / ∑ i = 1 m v k ( i ) v k ( i ) .

The v k ( i ) v k ( i + n ) term represents the correlation between the velocity at time i · Δ t and the velocity at time ( i + n ) · Δ t . v k ( i ) v k ( i ) is the correlation of the velocity with itself, and m is the total number of time steps over which the correlation will be computed. v k is the velocity associated with a specific wave vector in Fourier space defined as

(11) v k ( t ) = ∑ j u j ( t ) e ik x j 0 .

The u j ( t ) is the velocity vector of the j th atom at time t . The e ik x j 0 is the complex exponential function, where k = 2 π λ is the wave vector, and x j 0 is defined as the initial position or reference position of the j th atom. The wave vector ( k ) specifies the wave’s spatial frequency direction and is inversely related to the wavelength ( λ ) of the wave. By summing over all particles and multiplying each particle’s displacement u j ( t ) by the complex exponential factor e ik x j 0 , one can obtain the combined effect of each particle’s contribution to the velocity associated with wave vector k at time t [54]. To compute the power spectrum from the VACF, MD simulations were performed using periodic boundary conditions in a cubic box with an edge length of 200 Å using GROMACS software [39]. The simulations included a chain composed of 50 n-C4F10 reference molecules. The system’s energy was first minimized over 10,000 steps using the steepest descent algorithm. Then, an NPT simulation ran for 1.2 ns (nanoseconds) to adjust box length/density. Next, NVT simulations at T = 300 K were conducted using a box size from the previous NPT step to equilibrate the system further. After NVT equilibration, power spectra were calculated over 200 ps of analysis time. The temporal variation of the VACF results is shown in Figure 8(a). Figure 8(b) compares the VDOS results with the experimental infrared spectrum. The peak positions of the calculated VDOS closely correspond to those observed in the experimental infrared spectrum obtained from the study of Wang et al. [33].

Figure 8 (a) Temporal variation of the VACF. (b) VDOS or power spectrum of the PTFE chain (500–2,500 cm⁻¹) with experimental peak points shown by the red dashed lines.
Figure 8

(a) Temporal variation of the VACF. (b) VDOS or power spectrum of the PTFE chain (500–2,500 cm⁻¹) with experimental peak points shown by the red dashed lines.

The temporal variation of the VACF (Figure 8(a)) illustrates the evolving correlation between velocities over time. Experimental peak values, indicated by red dashed lines in Figure 8b, were compared with values obtained from MD simulations. Four prominent peaks were observed at wavenumbers 1,207, 1,151, 638, and 626 cm−1 in the experimental infrared spectrum of PTFE fibers [33]. The peak at 638 cm−1 in the experimental spectrum was attributed to a regular helix structure. In contrast, the peak at 626 cm−1 was linked to a helix-reversal defect in PTFE fibers, which was not observed in the MD simulation results [55]. The bands at 1,207 and 1,151 cm−1 were previously considered insensitive to the crystallinity level [56]. These bands have been attributed to the symmetric and asymmetric stretching vibrations of CF2 and C–C groups within the PTFE fibers. The computed peak positions of 1,189 and 1,132 cm−1 closely matched the experimental study’s peak positions of 1,207 and 1,151 cm−1, with deviations of 18 and 19 cm−1, respectively.

4.4 Specific heat capacity

The specific heat ( C p ( T ) ), or heat capacity per mass unit, was calculated based on the PTFE assemblies’ vibrational modes at constant volume across temperatures using QuantumATK. The expression of C p ( T ) is described by the following formula [57]:

(12) C p ( T ) = h 2 m k B T 2 ∫ 0 ∞ ν 2 exp h ν k B T exp h ν k B T − 1 2 g ( ν ) d ν ,

where T represents the temperature, ν denotes the vibrational frequency, h stands for Planck’s constant, m indicates the total mass of the atoms in the unit cell, k B represents Boltzmann’s constant, and g ( ν ) symbolizes the vibrational density of states, which describes how energy is distributed among vibrational modes [58]. The integral in the formula calculates the contribution of each vibrational mode to the specific heat, weighted by g ( ν ) . The fraction within the integral represents the population of each vibrational mode at temperature T, as described by the Bose–Einstein distribution. The factor, ℎ2 /(2πmk B T)2, positioned outside the integral, normalizes the units and scales the result appropriately. For this analysis, after the NPT equilibration described in the preceding section, MD simulations were executed under the NVT ensemble, wherein the temperature ranged from 0 to 800 K in increments of 100 K over a total duration of 3 ns, followed by a 1 ns duration at 800 K. After that, the temperature decreased to 300 K with the cooling rate of 4 K/ps and held for another 1 ns. Specific heat capacity was calculated during this entire MD trajectory using QuantumATK [48]. Our calculations yielded a heat capacity of 1.15 (J g−1 K−1) with a percent error of 4.5% based on MD simulations performed on four distinct assemblies of PTFE. This result closely aligns with the experimental findings of 1.10 (J g−1 K−1) reported by Furukawa et al. [34] (Figure 9). Additionally, Bhowmik et al. [23] conducted MD simulations using standard GAFF parameters [22] to predict the specific heat across various sizes of PTFE ensembles at only 300 K. Therefore, only 300 K comparisons were made. Their computational estimate was 1.37 (J g−1 K−1), with a reported percent error of 24.5%, significantly higher than our calculated value.

Figure 9 Comparison of computed and experimental specific heat capacity vs temperature for different ensembles of various sizes: [CF3-(C2F4)20-CF3]20, [CF3-(C2F4)40-CF3]40, [CF3-(C2F4)50-CF3]50, and [CF3-(C2F4)100-CF3]100.
Figure 9

Comparison of computed and experimental specific heat capacity vs temperature for different ensembles of various sizes: [CF3-(C2F4)20-CF3]20, [CF3-(C2F4)40-CF3]40, [CF3-(C2F4)50-CF3]50, and [CF3-(C2F4)100-CF3]100.

5 Conclusions

We introduce a new force field parameter set for PTFE, generated using the Paramfit protocol to optimize the bonded AMBER force field parameters. The optimization procedure involved refining conformational sets and fine-tuning the vdW parameters based on experimental data. These parameters showed excellent agreement with experimental data, particularly in reproducing the density and heat of vaporization of PTFE. The transferability of our force field parameters was demonstrated by simulating PTFE systems of different molecular weights. The resultant parameters exhibited high accuracy in predicting the density and specific heat capacity for various molecular weights of PTFE ensembles and the peak vibration spectrum values of the PTFE chain. This was coupled with the close agreement observed between the derived MM parameters and their corresponding QM references, as well as with experimental data. Overall, the force field parameters developed in this study represent a significant improvement over existing models in the literature, offering high accuracy and reliability for simulating PTFE and facilitating a better understanding of its behavior at the molecular level.

Acknowledgments

The computational results presented in this study were partly performed on Lehigh University Research Computing Infrastructure, the Sol and Hawk high-performance computing clusters. Hawk was made possible by NSF Grant 2019035.

  1. Funding information: The authors have stated that no funding was involved.

  2. Author contributions: Orhan Kaya: conceptualization, data curation, methodology, validation, visualization, formal analysis, and writing – original draft. Alparslan Oztekin: supervision, formal analysis, and writing – review and editing. Edmund B. Webb III: supervision, resources, formal analysis, writing – review and editing.

  3. Conflict of interest: The authors declare no conflict of interest.

  4. Ethical approval: The conducted research is not related to either human or animal use.

  5. Data availability statement: The AMBER force field parameters generated during the current study, as well as the parameters converted to LAMMPS and GROMACS formats, are available on Figshare and accessible via the following persistent web link: https://doi.org/10.6084/m9.figshare.26197325.v1.

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Received: 2024-05-14
Revised: 2024-07-06
Accepted: 2024-07-23
Published Online: 2024-08-08

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  5. Synthesis, characterization, in silico and in vitro studies of novel glycoconjugates as potential antibacterial, antifungal, and antileishmanial agents
  6. Sonochemical synthesis of gold nanoparticles mediated by potato starch: Its performance in the treatment of esophageal cancer
  7. Computational study of ADME-Tox prediction of selected phytochemicals from Punica granatum peels
  8. Phytochemical analysis, in vitro antioxidant and antifungal activities of extracts and essential oil derived from Artemisia herba-alba Asso
  9. Two triazole-based coordination polymers: Synthesis and crystal structure characterization
  10. Phytochemical and physicochemical studies of different apple varieties grown in Morocco
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  13. Evaluation of influence of Butea monosperma floral extract on inflammatory biomarkers
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https://doi.org/10.1515/chem-2024-0072
Keywords for this article
polytetrafluoroethylene; AMBER force field; parameter optimization; molecular dynamics simulation; density functional theory
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Porous silicon nanostructures: Synthesis, characterization, and their antifungal activity
  3. Biochar from de-oiled Chlorella vulgaris and its adsorption on antibiotics
  4. Phytochemicals profiling, in vitro and in vivo antidiabetic activity, and in silico studies on Ajuga iva (L.) Schreb.: A comprehensive approach
  5. Synthesis, characterization, in silico and in vitro studies of novel glycoconjugates as potential antibacterial, antifungal, and antileishmanial agents
  6. Sonochemical synthesis of gold nanoparticles mediated by potato starch: Its performance in the treatment of esophageal cancer
  7. Computational study of ADME-Tox prediction of selected phytochemicals from Punica granatum peels
  8. Phytochemical analysis, in vitro antioxidant and antifungal activities of extracts and essential oil derived from Artemisia herba-alba Asso
  9. Two triazole-based coordination polymers: Synthesis and crystal structure characterization
  10. Phytochemical and physicochemical studies of different apple varieties grown in Morocco
  11. Synthesis of multi-template molecularly imprinted polymers (MT-MIPs) for isolating ethyl para-methoxycinnamate and ethyl cinnamate from Kaempferia galanga L., extract with methacrylic acid as functional monomer
  12. Nutraceutical potential of Mesembryanthemum forsskaolii Hochst. ex Bioss.: Insights into its nutritional composition, phytochemical contents, and antioxidant activity
  13. Evaluation of influence of Butea monosperma floral extract on inflammatory biomarkers
  14. Cannabis sativa L. essential oil: Chemical composition, anti-oxidant, anti-microbial properties, and acute toxicity: In vitro, in vivo, and in silico study
  15. The effect of gamma radiation on 5-hydroxymethylfurfural conversion in water and dimethyl sulfoxide
  16. Hollow mushroom nanomaterials for potentiometric sensing of Pb2+ ions in water via the intercalation of iodide ions into the polypyrrole matrix
  17. Determination of essential oil and chemical composition of St. John’s Wort
  18. Computational design and in vitro assay of lantadene-based novel inhibitors of NS3 protease of dengue virus
  19. Anti-parasitic activity and computational studies on a novel labdane diterpene from the roots of Vachellia nilotica
  20. Microbial dynamics and dehydrogenase activity in tomato (Lycopersicon esculentum Mill.) rhizospheres: Impacts on growth and soil health across different soil types
  21. Correlation between in vitro anti-urease activity and in silico molecular modeling approach of novel imidazopyridine–oxadiazole hybrids derivatives
  22. Spatial mapping of indoor air quality in a light metro system using the geographic information system method
  23. Iron indices and hemogram in renal anemia and the improvement with Tribulus terrestris green-formulated silver nanoparticles applied on rat model
  24. Integrated track of nano-informatics coupling with the enrichment concept in developing a novel nanoparticle targeting ERK protein in Naegleria fowleri
  25. Cytotoxic and phytochemical screening of Solanum lycopersicum–Daucus carota hydro-ethanolic extract and in silico evaluation of its lycopene content as anticancer agent
  26. Protective activities of silver nanoparticles containing Panax japonicus on apoptotic, inflammatory, and oxidative alterations in isoproterenol-induced cardiotoxicity
  27. pH-based colorimetric detection of monofunctional aldehydes in liquid and gas phases
  28. Investigating the effect of resveratrol on apoptosis and regulation of gene expression of Caco-2 cells: Unravelling potential implications for colorectal cancer treatment
  29. Metformin inhibits knee osteoarthritis induced by type 2 diabetes mellitus in rats: S100A8/9 and S100A12 as players and therapeutic targets
  30. Effect of silver nanoparticles formulated by Silybum marianum on menopausal urinary incontinence in ovariectomized rats
  31. Synthesis of new analogs of N-substituted(benzoylamino)-1,2,3,6-tetrahydropyridines
  32. Response of yield and quality of Japonica rice to different gradients of moisture deficit at grain-filling stage in cold regions
  33. Preparation of an inclusion complex of nickel-based β-cyclodextrin: Characterization and accelerating the osteoarthritis articular cartilage repair
  34. Empagliflozin-loaded nanomicelles responsive to reactive oxygen species for renal ischemia/reperfusion injury protection
  35. Preparation and pharmacodynamic evaluation of sodium aescinate solid lipid nanoparticles
  36. Assessment of potentially toxic elements and health risks of agricultural soil in Southwest Riyadh, Saudi Arabia
  37. Theoretical investigation of hydrogen-rich fuel production through ammonia decomposition
  38. Biosynthesis and screening of cobalt nanoparticles using citrus species for antimicrobial activity
  39. Investigating the interplay of genetic variations, MCP-1 polymorphism, and docking with phytochemical inhibitors for combatting dengue virus pathogenicity through in silico analysis
  40. Ultrasound induced biosynthesis of silver nanoparticles embedded into chitosan polymers: Investigation of its anti-cutaneous squamous cell carcinoma effects
  41. Copper oxide nanoparticles-mediated Heliotropium bacciferum leaf extract: Antifungal activity and molecular docking assays against strawberry pathogens
  42. Sprouted wheat flour for improving physical, chemical, rheological, microbial load, and quality properties of fino bread
  43. Comparative toxicity assessment of fisetin-aided artificial intelligence-assisted drug design targeting epibulbar dermoid through phytochemicals
  44. Acute toxicity and anti-inflammatory activity of bis-thiourea derivatives
  45. Anti-diabetic activity-guided isolation of α-amylase and α-glucosidase inhibitory terpenes from Capsella bursa-pastoris Linn.
  46. GC–MS analysis of Lactobacillus plantarum YW11 metabolites and its computational analysis on familial pulmonary fibrosis hub genes
  47. Green formulation of copper nanoparticles by Pistacia khinjuk leaf aqueous extract: Introducing a novel chemotherapeutic drug for the treatment of prostate cancer
  48. Improved photocatalytic properties of WO3 nanoparticles for Malachite green dye degradation under visible light irradiation: An effect of La doping
  49. One-pot synthesis of a network of Mn2O3–MnO2–poly(m-methylaniline) composite nanorods on a polypyrrole film presents a promising and efficient optoelectronic and solar cell device
  50. Groundwater quality and health risk assessment of nitrate and fluoride in Al Qaseem area, Saudi Arabia
  51. A comparative study of the antifungal efficacy and phytochemical composition of date palm leaflet extracts
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  53. Specialized compounds of four Cameroonian spices: Isolation, characterization, and in silico evaluation as prospective SARS-CoV-2 inhibitors
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  57. Wild Thymus zygis L. ssp. gracilis and Eucalyptus camaldulensis Dehnh.: Chemical composition, antioxidant and antibacterial activities of essential oils
  58. 3D-QSAR, molecular docking, ADMET, simulation dynamic, and retrosynthesis studies on new styrylquinolines derivatives against breast cancer
  59. Deciphering the influenza neuraminidase inhibitory potential of naturally occurring biflavonoids: An in silico approach
  60. Determination of heavy elements in agricultural regions, Saudi Arabia
  61. Synthesis and characterization of antioxidant-enriched Moringa oil-based edible oleogel
  62. Ameliorative effects of thistle and thyme honeys on cyclophosphamide-induced toxicity in mice
  63. Study of phytochemical compound and antipyretic activity of Chenopodium ambrosioides L. fractions
  64. Investigating the adsorption mechanism of zinc chloride-modified porous carbon for sulfadiazine removal from water
  65. Performance repair of building materials using alumina and silica composite nanomaterials with electrodynamic properties
  66. Effects of nanoparticles on the activity and resistance genes of anaerobic digestion enzymes in livestock and poultry manure containing the antibiotic tetracycline
  67. Effect of copper nanoparticles green-synthesized using Ocimum basilicum against Pseudomonas aeruginosa in mice lung infection model
  68. Cardioprotective effects of nanoparticles green formulated by Spinacia oleracea extract on isoproterenol-induced myocardial infarction in mice by the determination of PPAR-γ/NF-κB pathway
  69. Anti-OTC antibody-conjugated fluorescent magnetic/silica and fluorescent hybrid silica nanoparticles for oxytetracycline detection
  70. Curcumin conjugated zinc nanoparticles for the treatment of myocardial infarction
  71. Identification and in silico screening of natural phloroglucinols as potential PI3Kα inhibitors: A computational approach for drug discovery
  72. Exploring the phytochemical profile and antioxidant evaluation: Molecular docking and ADMET analysis of main compounds from three Solanum species in Saudi Arabia
  73. Unveiling the molecular composition and biological properties of essential oil derived from the leaves of wild Mentha aquatica L.: A comprehensive in vitro and in silico exploration
  74. Analysis of bioactive compounds present in Boerhavia elegans seeds by GC-MS
  75. Homology modeling and molecular docking study of corticotrophin-releasing hormone: An approach to treat stress-related diseases
  76. LncRNA MIR17HG alleviates heart failure via targeting MIR17HG/miR-153-3p/SIRT1 axis in in vitro model
  77. Development and validation of a stability indicating UPLC-DAD method coupled with MS-TQD for ramipril and thymoquinone in bioactive SNEDDS with in silico toxicity analysis of ramipril degradation products
  78. Biosynthesis of Ag/Cu nanocomposite mediated by Curcuma longa: Evaluation of its antibacterial properties against oral pathogens
  79. Development of AMBER-compliant transferable force field parameters for polytetrafluoroethylene
  80. Treatment of gestational diabetes by Acroptilon repens leaf aqueous extract green-formulated iron nanoparticles in rats
  81. Development and characterization of new ecological adsorbents based on cardoon wastes: Application to brilliant green adsorption
  82. A fast, sensitive, greener, and stability-indicating HPLC method for the standardization and quantitative determination of chlorhexidine acetate in commercial products
  83. Assessment of Se, As, Cd, Cr, Hg, and Pb content status in Ankang tea plantations of China
  84. Effect of transition metal chloride (ZnCl2) on low-temperature pyrolysis of high ash bituminous coal
  85. Evaluating polyphenol and ascorbic acid contents, tannin removal ability, and physical properties during hydrolysis and convective hot-air drying of cashew apple powder
  86. Development and characterization of functional low-fat frozen dairy dessert enhanced with dried lemongrass powder
  87. Scrutinizing the effect of additive and synergistic antibiotics against carbapenem-resistant Pseudomonas aeruginosa
  88. Preparation, characterization, and determination of the therapeutic effects of copper nanoparticles green-formulated by Pistacia atlantica in diabetes-induced cardiac dysfunction in rat
  89. Antioxidant and antidiabetic potentials of methoxy-substituted Schiff bases using in vitro, in vivo, and molecular simulation approaches
  90. Anti-melanoma cancer activity and chemical profile of the essential oil of Seseli yunnanense Franch
  91. Molecular docking analysis of subtilisin-like alkaline serine protease (SLASP) and laccase with natural biopolymers
  92. Overcoming methicillin resistance by methicillin-resistant Staphylococcus aureus: Computational evaluation of napthyridine and oxadiazoles compounds for potential dual inhibition of PBP-2a and FemA proteins
  93. Exploring novel antitubercular agents: Innovative design of 2,3-diaryl-quinoxalines targeting DprE1 for effective tuberculosis treatment
  94. Drimia maritima flowers as a source of biologically potent components: Optimization of bioactive compound extractions, isolation, UPLC–ESI–MS/MS, and pharmacological properties
  95. Estimating molecular properties, drug-likeness, cardiotoxic risk, liability profile, and molecular docking study to characterize binding process of key phyto-compounds against serotonin 5-HT2A receptor
  96. Fabrication of β-cyclodextrin-based microgels for enhancing solubility of Terbinafine: An in-vitro and in-vivo toxicological evaluation
  97. Phyto-mediated synthesis of ZnO nanoparticles and their sunlight-driven photocatalytic degradation of cationic and anionic dyes
  98. Monosodium glutamate induces hypothalamic–pituitary–adrenal axis hyperactivation, glucocorticoid receptors down-regulation, and systemic inflammatory response in young male rats: Impact on miR-155 and miR-218
  99. Quality control analyses of selected honey samples from Serbia based on their mineral and flavonoid profiles, and the invertase activity
  100. Eco-friendly synthesis of silver nanoparticles using Phyllanthus niruri leaf extract: Assessment of antimicrobial activity, effectiveness on tropical neglected mosquito vector control, and biocompatibility using a fibroblast cell line model
  101. Green synthesis of silver nanoparticles containing Cichorium intybus to treat the sepsis-induced DNA damage in the liver of Wistar albino rats
  102. Quality changes of durian pulp (Durio ziberhinus Murr.) in cold storage
  103. Study on recrystallization process of nitroguanidine by directly adding cold water to control temperature
  104. Determination of heavy metals and health risk assessment in drinking water in Bukayriyah City, Saudi Arabia
  105. Larvicidal properties of essential oils of three Artemisia species against the chemically insecticide-resistant Nile fever vector Culex pipiens (L.) (Diptera: Culicidae): In vitro and in silico studies
  106. Design, synthesis, characterization, and theoretical calculations, along with in silico and in vitro antimicrobial proprieties of new isoxazole-amide conjugates
  107. The impact of drying and extraction methods on total lipid, fatty acid profile, and cytotoxicity of Tenebrio molitor larvae
  108. A zinc oxide–tin oxide–nerolidol hybrid nanomaterial: Efficacy against esophageal squamous cell carcinoma
  109. Research on technological process for production of muskmelon juice (Cucumis melo L.)
  110. Physicochemical components, antioxidant activity, and predictive models for quality of soursop tea (Annona muricata L.) during heat pump drying
  111. Characterization and application of Fe1−xCoxFe2O4 nanoparticles in Direct Red 79 adsorption
  112. Torilis arvensis ethanolic extract: Phytochemical analysis, antifungal efficacy, and cytotoxicity properties
  113. Magnetite–poly-1H pyrrole dendritic nanocomposite seeded on poly-1H pyrrole: A promising photocathode for green hydrogen generation from sanitation water without using external sacrificing agent
  114. HPLC and GC–MS analyses of phytochemical compounds in Haloxylon salicornicum extract: Antibacterial and antifungal activity assessment of phytopathogens
  115. Efficient and stable to coking catalysts of ethanol steam reforming comprised of Ni + Ru loaded on MgAl2O4 + LnFe0.7Ni0.3O3 (Ln = La, Pr) nanocomposites prepared via cost-effective procedure with Pluronic P123 copolymer
  116. Nitrogen and boron co-doped carbon dots probe for selectively detecting Hg2+ in water samples and the detection mechanism
  117. Heavy metals in road dust from typical old industrial areas of Wuhan: Seasonal distribution and bioaccessibility-based health risk assessment
  118. Phytochemical profiling and bioactivity evaluation of CBD- and THC-enriched Cannabis sativa extracts: In vitro and in silico investigation of antioxidant and anti-inflammatory effects
  119. Investigating dye adsorption: The role of surface-modified montmorillonite nanoclay in kinetics, isotherms, and thermodynamics
  120. Antimicrobial activity, induction of ROS generation in HepG2 liver cancer cells, and chemical composition of Pterospermum heterophyllum
  121. Study on the performance of nanoparticle-modified PVDF membrane in delaying membrane aging
  122. Impact of cholesterol in encapsulated vitamin E acetate within cocoliposomes
  123. Review Articles
  124. Structural aspects of Pt(η3-X1N1X2)(PL) (X1,2 = O, C, or Se) and Pt(η3-N1N2X1)(PL) (X1 = C, S, or Se) derivatives
  125. Biosurfactants in biocorrosion and corrosion mitigation of metals: An overview
  126. Stimulus-responsive MOF–hydrogel composites: Classification, preparation, characterization, and their advancement in medical treatments
  127. Electrochemical dissolution of titanium under alternating current polarization to obtain its dioxide
  128. Special Issue on Recent Trends in Green Chemistry
  129. Phytochemical screening and antioxidant activity of Vitex agnus-castus L.
  130. Phytochemical study, antioxidant activity, and dermoprotective activity of Chenopodium ambrosioides (L.)
  131. Exploitation of mangliculous marine fungi, Amarenographium solium, for the green synthesis of silver nanoparticles and their activity against multiple drug-resistant bacteria
  132. Study of the phytotoxicity of margines on Pistia stratiotes L.
  133. Special Issue on Advanced Nanomaterials for Energy, Environmental and Biological Applications - Part III
  134. Impact of biogenic zinc oxide nanoparticles on growth, development, and antioxidant system of high protein content crop (Lablab purpureus L.) sweet
  135. Green synthesis, characterization, and application of iron and molybdenum nanoparticles and their composites for enhancing the growth of Solanum lycopersicum
  136. Green synthesis of silver nanoparticles from Olea europaea L. extracted polysaccharides, characterization, and its assessment as an antimicrobial agent against multiple pathogenic microbes
  137. Photocatalytic treatment of organic dyes using metal oxides and nanocomposites: A quantitative study
  138. Antifungal, antioxidant, and photocatalytic activities of greenly synthesized iron oxide nanoparticles
  139. Special Issue on Phytochemical and Pharmacological Scrutinization of Medicinal Plants
  140. Hepatoprotective effects of safranal on acetaminophen-induced hepatotoxicity in rats
  141. Chemical composition and biological properties of Thymus capitatus plants from Algerian high plains: A comparative and analytical study
  142. Chemical composition and bioactivities of the methanol root extracts of Saussurea costus
  143. In vivo protective effects of vitamin C against cyto-genotoxicity induced by Dysphania ambrosioides aqueous extract
  144. Insights about the deleterious impact of a carbamate pesticide on some metabolic immune and antioxidant functions and a focus on the protective ability of a Saharan shrub and its anti-edematous property
  145. A comprehensive review uncovering the anticancerous potential of genkwanin (plant-derived compound) in several human carcinomas
  146. A study to investigate the anticancer potential of carvacrol via targeting Notch signaling in breast cancer
  147. Assessment of anti-diabetic properties of Ziziphus oenopolia (L.) wild edible fruit extract: In vitro and in silico investigations through molecular docking analysis
  148. Optimization of polyphenol extraction, phenolic profile by LC-ESI-MS/MS, antioxidant, anti-enzymatic, and cytotoxic activities of Physalis acutifolia
  149. Phytochemical screening, antioxidant properties, and photo-protective activities of Salvia balansae de Noé ex Coss
  150. Antihyperglycemic, antiglycation, anti-hypercholesteremic, and toxicity evaluation with gas chromatography mass spectrometry profiling for Aloe armatissima leaves
  151. Phyto-fabrication and characterization of gold nanoparticles by using Timur (Zanthoxylum armatum DC) and their effect on wound healing
  152. Does Erodium trifolium (Cav.) Guitt exhibit medicinal properties? Response elements from phytochemical profiling, enzyme-inhibiting, and antioxidant and antimicrobial activities
  153. Integrative in silico evaluation of the antiviral potential of terpenoids and its metal complexes derived from Homalomena aromatica based on main protease of SARS-CoV-2
  154. 6-Methoxyflavone improves anxiety, depression, and memory by increasing monoamines in mice brain: HPLC analysis and in silico studies
  155. Simultaneous extraction and quantification of hydrophilic and lipophilic antioxidants in Solanum lycopersicum L. varieties marketed in Saudi Arabia
  156. Biological evaluation of CH3OH and C2H5OH of Berberis vulgaris for in vivo antileishmanial potential against Leishmania tropica in murine models
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