Molecular Simulation of Polyphosphazenes - ACS Symposium Series

Chapter 11

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Molecular Simulation of Polyphosphazenes Joel R. Fried* Department of Chemical Engineering, University of Louisville, Ernst Hall 106, Louisville, Kentucky 40292, United States *E-mail: [email protected]

The use of molecular simulation, including molecular dynamics and Monte Carlo methods, in the study of polyphosphazenes is reviewed. The development and validation of the Class II force field COMPASS is discussed with examples on its utility for predicting physical and thermal properties such as density, permeability, and the glass transition temperature. Applications for the use of molecular simulations in the study of polyphosphazenes that are reviewed include polymer electrolytes, gas-separation membranes, and biomedical materials.

Over 700 poly(organophosphazene)s have been synthesized based on the general structure shown in Figure 1. The substituent groups, R1 and R2, can be any of a large number of substituent groups such as an alkoxy, alkyl, or amine group. The nature of the substituent group has significant control on the properties of the polyphosphazene including the glass transition temperature (Tg), degree of crystallinity, and gas permeability. Values of Tg can vary from 173 to 423 K (1). Poly-phosphazenes having aromatic-amine substituent groups typically have the highest Tg (2). Some semicrystalline polyphosphazenes exhibit both a crystalline melting temperature (Tm) and a sub-Tm transition, T(l), that marks a transition from a crystalline to a mesophasic state.

© 2018 American Chemical Society Andrianov and Allcock; Polyphosphazenes in Biomedicine, Engineering, and Pioneering Synthesis ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Figure 1. Generic structure of a repeating unit of a polyphosphazene where R1 and R2 represent substituent groups. This chapter focuses on the use of molecular simulations to investigate properties of polyphosphazenes such as intermolecular interactions, density, diffusivity, sorption, and Tg. Applications include a wide range of important uses such as fuel cells, polymer electrolytes, membrane separations, and controlled drug release. In order to investigate such properties using atomistic molecular simulations, it is necessary to have a well-parameterized and extensively validated molecular mechanics force field. The COMPASS (3) (Condensed-phase Optmized Molecular Potentials for Atomistic Simulation Studies) force field is one that has been well-parameterized and validated for polyphosphazenes as discussed in the following section.

Development of the COMPASS Force Field for Polyphosphazenes The first step toward the parameterization of the COMPASS force field was an ab initio study of the structure of polyphosphazenes. This was accomplished by Sun (4) who used density functional (DFT) calculations of trimers to study polyphosphazene structure and conformations. One conclusion from that study was that the P–N bonding of the main chain consists of an ionic s- and a p-bond induced primarily by negative hyperconjugation with charges on P and N close to +1 and –1, respectively. This type of bonding results in a very flexible polymer chain with rotational barriers comparable to that of the C–C bond in ethane (ca. 2 kcal/mol). This high mobility results in low Tg and high permeability of polyphosphazenes that approaches that of poly-siloxanes (5). COMPASS is classified as a Class II force field that had been derived from the earlier force fields such as the Consistent Force Field (CFF), the Consistent Valence Force Field (CVFF), and its most important derivative, the Polymer Consistent Force Field (pcff). The functional forms of COMPASS are the same as CFF93 (6, 7) given as

242 Andrianov and Allcock; Polyphosphazenes in Biomedicine, Engineering, and Pioneering Synthesis ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

where the potential energy, E, has two contributions—bonded terms and non-bonded terms. The bonded terms include potential terms for bond-stretching (b), angle-bending (θ), and torsion (φ). COMPASS also includes a term for improper torsion (i.e., out-of-plane, χ). The bond-stretching and angle-bending terms in COMPASS are quartic. Charges and bonded terms had been derived from Hartree Fock (HF/6-31G*) quantum chemical calculations in the parent force fields. Non-bonded terms were initially transferred from pcff and optimized using MD simulations of condensed-phase properties. Characteristic of Class II force fields is a large number of cross terms that reflect the coupling of different potential motions such as bond stretching and angle bending (e.g., Ebθ) on contiguous bonds. These cross-coupling terms are important for predicting vibrational frequencies and structure variations associated with conformational changes. The non-bonded terms are traditionally electrostatic (identified as elec) and steric, typically Lennard-Jones (LJ). The electrostatic contribution is in the form of a Coulombic term while the LJ term is a 6-9 potential compared to the more commonly used but less accurate 6-12 potential. For the electrostatic contributions, the net partial charge of an atom, qi, is obtained as a summation of all charge bond-increments, δij, related to the specific atom as

The parameterization of COMPASS for phosphazenes was accom-plished by a collaboration of Sun, Ren, and Fried (8). Details of the parameterization procedures are given in that publication. Validations included comparisons of structural parameters, vibrational frequencies, X-ray data, conformational energies, and densities with experimental data and DFT calculations. Of importance in regards to subsequent discussion, molecular dynamics (MD) simulations of isomers of poly(butoxyphosphazenes) were used to predict density and Tg for comparison with experimental data. These amorphous polyphos-phazenes were selected due to their amorphous character and the availability of good experimental data (9), especially for density and Tg. For poly(di-n-butoxyphosphazene (PnBuP) and poly(di-sec-butoxyphos-phazene) (PsBuP), bond lengths, bond angles, and torsional angles agreed well with X-ray data and Tgs obtained by NPT MD agreed well with results from thermal analysis (8). Simulated values of density and Tg for the a isomer, poly(di-i-butoxyphosphazene) (PiBuP), were reported to be in good agreement with experimental values in a subsequent publication by Fried and Ren (10). As shown in Table I, there is excellent agreement between simulated and experimental values (DSC measurements) of Tg for the three isomers. A comprehensive study of the Tg of the polybutoxyphosphazenes as well as poly[bis(2,2,2-trifluoroethoxy)phosphazene] (PTFEP) have been given by Fried and Ren (11).


Table I. Structures and Values of Density and Tg of Three Isomers of Poly(butoxy phosphazenes) and Poly[bis(2,2,2-trifluoroethoxy)phosphazene] (PTFEP)

Many of the simulation studies reported in this chapter used the COMPASS force field. A review of COMPASS as well as several other force fields that have been used in the simulation of polyphosphazenes and other polymers has been given by Fried (12). COMPASS has also been used successfully by our group for the molecular simulation of phosphoric acid (13). An updated version of COMPASS (COMPASS II) extends coverage to include additional polymers and drug-like molecules while initial parameterization is conserved (14). Other force fields that have been used in the simulation of polyphosphazenes are CHARMm (15), AMBER (16). DREIDING (17), and UFF (18) as discussed in subsequent sections. It is noted that CHARMm and AMBER are the most widely used force fields for the molecular simulation of biological materials including proteins, carbohydrates, and nucleic acids. The form of these force fields have been reviewed in the previously cited publication (12). Since these force fields were not parameterized for polymers, parameters in CHARMm and AMBER were separately developed for each polyphosphazene. Different force fields that have been used in the molecular simulation studies of polyphosphazenes (10, 19–34) are identified in Table II.


Table II. Molecular Simulation Studies of Polyphosphazenes Polymer

Force Field/ Method

Comments

Ref

PnBuPa, PsBuPb, PiBuPc

COMPASS

MD simulation of gas permeability

(10)

PTFEPd

COMPASS

Gas permeability simulation Specific CO2 interactions

PDCPe

ADMP COMPASS AMBER CHARMm

Ab-initio MD of hydrolysis Conformational model Crystal structure Parameterization of CHARMm

(22) (23) (24) (25)

oligomersf

Custom FF

Conformational analysis

(26)

PMPPg

CHARMm

Combined X-ray/MD study

(27)

P-DPNPh

CHARMm

Combined X-ray/MD study

(28)

PDOBPNI

AMBER

Thermal degradation, solution properties

(29)

Copolymerj

AMBER

Analysis of secondary structure

(30)

MEEPk

COMPASS

Li+ transport

(31)

PBMPl

COMPASS

Direct methanol fuel cell

(20)

MPm

DREIDING

Ion diffusion

(32)

MEEP-like

AMBER

Ionic conduction

(33)

MEEP-like

UFF DREIDING

Li+ distribution in a polyphosphazene mixture

(34)

(19–21)

a PnBuP, poly(di-n-butoxyphosphazene. b PsBuP, poly(di-sec-butoxyphosphazene). c PiBuP, poly(di-i-butoxyphosphazene). d PTFEP, poly-[bis(2,2,2)trifluoroethoxyphosphazene]. e PDCP, poly[bis(chloro)phos-phazene]. f chloroand difluorophosphazenes]. g PMPP, poly[di(4-methylphenoxy)phosphazene]. h P-DBNP, poly(2.2′-dioxy-1,1′-binaph-thyl)phosphazene). I PDOBPN, poly(2,2′-dioxybiphenylphosphazene). j copolymer of phenoxy and binaphthoxy chromophoric groups. k MEEP, poly[bis(2-(2-methoxyethoxy)ethoxy)phosphazenes]. l PBMP, poly[bis(3-methylphenoxy)phosphazene]. m MP, poly[bis(2-(2′methoxyl)phospha-zene].

Molecular Simulations of Polyphosphazenes There are many applications for polyphosphazenes. For example, their high permeability makes polyphosphazenes attractive as mem-branes for gas, liquid, and vapor separations. Other important uses for polyphosphazenes include controlled drug delivery, micro-encapsula-tion, polymer electrolytes, non-linear optical and electro-optic materials, and proton-exchange membranes for direct methanol fuel cells. For many of these applications, molecular simulations have provided impor-tant insight into polyphosphazene function as discussed in 245 Andrianov and Allcock; Polyphosphazenes in Biomedicine, Engineering, and Pioneering Synthesis ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

the following sections. Detailed reviews that address molecular simulations of poly-phosphazenes are provided in two other sources (35, 36).

Polymer Electrolytes Following the discovery of ion conduction in poly(ethylene oxide) in 1973 by Wright (37), there has been interest in looking at polymers with similar chemical structure that could provide attractive performance. One polyphosphazene structure that has attracted interest is poly[bis(2-(2methoxyethoxy)ethoxy)phosphazene] (MEEP) whose structure is shown in Figure 2. There have been a number of simulation studies using different force fields to look at ion transport and ion coordination in polyphosphazenes (31–34). Several of these studies were cited in Table II. A more review of transport in polymer electrolytes is given by Fried (35). One study by Luther et al. (31) utilized both spectroscopic and MD simulation (COMPASS force field). This simulation employed 20-mer chains and focused on the coordination of Li+ with MEEP. A mechanism generally proposed for ionic transport in MEEP is that Li+ association is limited to the oxygen nuclei on the substituent group. The study by Luther et al. (31) showed that lithium association also occurs with the nitrogen nuclei of the polymer backbone. They suggested that the association is probably a coordination between the nitrogen nuclei and the oxygen nuclei of the substituent groups as illustrated in Figure 3.

Figure 2. Chemical structure of MEEP.

Figure 3. Lithium association with MEEP. 246 Andrianov and Allcock; Polyphosphazenes in Biomedicine, Engineering, and Pioneering Synthesis ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Gas-Separation Membranes A comprehensive review of the molecular simulation of gas and vapor transport in highly permeable polymers, including polyphosphazenes, has been given by Fried (36). A review of the simulation of gas diffusion and solubility specifically for poly(organophosphazenes) appears in another review (38). Due to the high flexibility of the polyphosphazene chain and low Tg, the permeability of polyphosphazenes is among the highest of all major classes of polymers with the exception of polysiloxanes and poly[1-(trimethylsilyl)-1-propyne] (PTMSP) which is a glassy nanoporous polymer. In terms of simulation of gas transport properties, the most extensively studied polyphosphazenes have been the isomers of polybutoxyphosphazenes, mentioned earlier in reference to force field validation, and poly[bis(2,2,2-trifluoroethoxy)phosphazene] or PTFEP whose structure is shown in Table I.

Poly(dibutoxyphosphazenes) A detailed molecular simulation study of gas permeability of all three amorphous poly(dibutoxyphosphazenes), PnBuP, PsBuP, and PiBuP (see Table I for structures) using the COMPASS force field parameter-ized for phosphazenes (8) was made by Fried and Ren (10). The permeability coefficient is a product of the solubility (S) and diffusivity (D) coefficients of the penetrant (P = DS). Both S and D can be obtained from molecular simulation. In the study by Fried and Ren, the gas diffusion coefficient (D) of six gases (He, Ne, O2. N2, CO2, and CH4) were obtained from NVT molecular dynamics by use of the Einstein relationship written in the form

where Nα is the number of diffusing particles of type α, ri(0) and r(t) are the initial and final positions of the center of mass of particle i over the time interval t, and is the mean-square displacement (MSD) averaged over the ensemble. The diffusion coefficients followed the correlation given by Toi (39) as

where K1 and K2 are constants and deff is the effective diameter of the gas molecule. The solubility coefficients were obtained by using the Grand Canonical Monte Carlo (GCMC) method that measures the concentration of sorbed gas (C) and S was obtained from the limiting slope of the sorption isotherm at zero pressure as


where C is in units of cm3(STP)/cm3 polymer and p is pressure. The solubility coefficients obtained in this way followed the correlation proposed by Teplyakov and Meares (40) given as

where So is a constant and the ratio of the gas.

is the Lennard-Jones potential well depth

Poly[bis(2,2,2-trifluoroethoxy)phosphazene] Following the earlier simulation study of gas diffusion and solubility in poly(dibutoxyphosphazenes), Hu and Fried (19) reported results of molecu-lar simulation of diffusion and solubility of seven gases (He, H2, O2. N2, CH4, CO2, and Xe) in PTFEP. Since PTFEP is semicrystalline, gas diffusion and solubility were obtained in an amorphous cell and in all α-orthorhombic crystalline cell of PTFEP. The COMPASS force field was also used in this study. Diffusion and solubility coefficient were obtained by use of eqs. (3) and (5), respectively. It was shown that only He showed any solubility in the α-orthorhombic crystalline cells of PTFEP although diffusion was unrestricted. It was noted in this study that the solubility coefficient for CO2 was elevated compared to the prediction expected by applying the correlation given by eq (6) to the other six gas molecules. Similar observations have been made for sorbed CO2 in other fluorine-containing polymers. As shown by Fried and Hu (21), the cause of this elevated CO2 solubility is a moderately strong dipole–quadrupole interaction (-11.5 kJ mol-1) involving the polar fluoroethoxy group and a strong CO2 quadrupole (21). The nature of this interaction was supported by both MD simulation (RDF) and high-level ab-initio calculations MP2/6-311++G**) in that study.

Polyphosphazenes for Biomedical Applications Kroger and Fried (23) have reported a detailed molecular simulation of poly(dichlorophosphazne) (PDCP), both crystalline and amorphous state, poly(glycinethylesterphosphazene) (PGEEP), poly[bis(carbonylatophenoxy)phosphazene) (PCPP), and poly[di(imidoazole)phosphazene] (PDIP). Chemical structures, Tgs, densities, and solubility parameters are given in Table III. The COMPASS force field was used to obtain density, Tg, and the solubility parameter (obtained from the cohesive energy density, CED), as well as time-correction functions that provided information concerning the flexibility of the P–N backbones and side chains.


Table III. Structures and Properties of Biomedically Relevant Polyphosphazenes

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Molecular Simulation of Polyphosphazenes - ACS Symposium Series

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