Dimethyl Ether Polymers Based on Molecular Dynamics Simulations

Apr 30, 2013 - ABSTRACT: Poly(ethylene glycol) dimethyl ether (PEGDME) polymers are ... we systematically investigate structure, aggregate state, and ...
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Some Insight into Stability of Amorphous Poly(ethylene glycol) Dimethyl Ether Polymers Based on Molecular Dynamics Simulations Jinjian Wang, Yin Wang, Xiaolei Zhu,* and Xiaohua Lu* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing University of Technology, Nanjing 210009, China S Supporting Information *

ABSTRACT: Poly(ethylene glycol) dimethyl ether (PEGDME) polymers are widely used as drug solid dispersion reagents. They can cause the amorphization of drugs and improve their solubility, stability, and bioavailability. However, the mechanism about why amorphous PEGDME 2000 polymer is highly stable is unclear so far. Molecular dynamics (MD) simulation is a unique key technique to solve it. In the current work, we systematically investigate structure, aggregate state, and thermodynamic and kinetic behaviors during the phase-transition processes of the PEGDME polymers with different polymerization degree in terms of MD simulations. The melting and glass-transition temperatures of the polymers are in good agreement with experimental values. The amorphous PEGDME2000 exhibits high stability, which is consistent with the recent experiment results and can be ascribed to a combination of two factors, that is, a high thermodynamic driving force for amorphization and a relatively low molecular mobility. SECTION: Glasses, Colloids, Polymers, and Soft Matter

T

there are no deep theoretical explanations for these surprising results. If we can provide reasonable explanations about the above experimental results based on molecular dynamics (MD) simulations, it will be helpful for designing the new drugs or drug solid dispersion reagents with similar properties to PEGDME2000 and speeding up the experimental studies. We systematically investigate thermodynamic and dynamic behaviors during the phase-transition processes of PEGDME polymers with different polymerization degree using MD simulations. In the current work, the findings are as follows: (i) the relationship between the glass-transition temperature (Tg) and polymerization degree (n) agrees with Ellis’ equation very well; (ii) the simulated phase-transition temperatures (Tg and Tm) are in good agreement with experimental ones (Tg and Tm), which reveals the reliability of simulated results; (iii) the analysis results of different interaction components during the glass-transition process suggest that the torsional and electrostatic interactions play roles in the glass-transition process; and (iv) the high stability of the amorphous PEGDME2000 can be attributed to its higher configurational entropy and low molecular mobility. The current work provides the reasonable explanations for recent experimental results.10 We examine here the stabilization mechanism of PEGDME2000. The molecular structure and physical properties of selected PEGDME systems are shown in Figure S1 and Table S1 (Supporting Information (SI)), respectively. The

he transformation of the crystalline drugs into amorphous ones can significantly improve drug solubility and bioavailability.1,2 Unfortunately, normally, the amorphous drugs are thermodynamically unstable and tend to transfer into crystalline ones during drug storage process, which will greatly decrease drug solubility and bioavailability. However, great progress has been made toward adding some solid dispersion reagents (for example, polymers) into drugs since the solid dispersion technique has been developed.3−7 The drug solid dispersion technique plays a crucial role in improving drug stability, solubility, and bioavailability. Although many experimental and theoretical investigations have been reported,3−7 a fundamental understanding of the factors controlling stability of drug solid dispersion remains controversial. The poly(ethylene glycol) dimethyl ether (PEGDME) has been used as a drug carrier in clinical and medicinal fields.8,9 Recently, Sadowski et al.10 observed oilingout behavior during the crystallization of PEGDME2000 from diethyl ketone, ethyl acetate, and 2-propanol, whereas no oiling out was detected during the cooling process of PEGDME1000 from the solvents considered. In the work performed by Sadowski et al.,10 an interesting and important result is that the liquid−liquid line locates below the solid−liquid line for PEGDME2000/solvent. Here one of two phases for the liquid−liquid line is liquid PEGDME2000, which suggests that liquid PEGDME2000 will preferentially transfer into amorphous solid instead of crystalline solid. As previously mentioned, usually, amorphous solid is unstable thermodynamically and tends to transfer into crystalline solid, but it is not the case for PEGDME2000. To the best our knowledge, © 2013 American Chemical Society

Received: April 26, 2013 Accepted: April 30, 2013 Published: April 30, 2013 1718

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Figure 1. Snapshots of equilibrium configurations of PEGDME 350 in various stages of heating and cooling. Heating process (top): (a) 125, (b) 275, (c) 575, and (d) 725 K; cooling process (bottom): (e) 725, (f) 575, (g) 275, and (h) 125 K. The gray and red balls represent carbon and oxygen atoms, respectively (in which we ignore hydrogen atoms).

determined based on glass-transition temperature (Tg).14 The glass-transition of polymers is usually examined under isobaric conditions, during which the thermodynamic variables, such as, enthalpy, potential energy, volume, and so on, vary with temperature. As represented in Figure 3, each of the ν−T curves exhibit slope change at some temperature, which reveals the glass transition. The slope change in the ν−T curve can be used to determine the glass-transition temperature Tg.15 The melting and glass-transition temperatures are listed in Table S3 (SI). As shown in Table S3 (SI), the glass-transition temperature increases as the polymerization degree increases, as expected. The Tg of polymer varies with polymerization degree (n) according to the following empirical relation, originally proposed by Fox and Flory.16,17

details of MD simulations and potential parameters are in the SI and Table S2. First, we examine the structures of PEGDME350 polymer during cooling and heating processes. During heating and cooling stages, the images of projections of the atoms in PEGDME350 are displayed in Figure 1. Before the melting temperature, the PEGDME350 has ordered structures (Figures 1a,b). After the melting and cooling processes, the PEGDME350 polymer exhibits disordered structures (Figure 1c−h). The order degrees of a polymer chain are analyzed by bond length, bond angle, dihedral,11 and chain end-to-end12 distributions in the SI (S2, Figures S2−S4). The whole polymer is characterized by the global orientational order parameter (P2)13 in the SI (S2, Figure S5). The above results demonstrate that the potential model used in current work can capture the conformation of polymer chain and aggregate states of PEGDME polymers. To examine the phase transition of PEGDME polymers during the heating process, we show the nonbond energies of some selected systems as a function of temperature in Figure 2. In Figure 2, there are significant energy jumps, which reveal the melting transition of PEGDME polymers. On the basis of Figure 2, we can estimate the melting temperatures (Tm). During cooling processes of the melted PEGDME polymers, the molecular rearrangement rate in supercooled liquid can be

Tg = Tg, ∞ −

Kg n

(1)

where Tg,∞ is the asymptotic value of Tg for infinite chain length and Kg is an empirical constant. Equation 1 usually describes experimental data well (if the molecular weight is not too small).18 A better description of the relationship between Tg and n for polymers is suggested by Ellis.19 Kg n n = 2 + Tg Tg, ∞ Tg, ∞

(2)

It is easy to note from Figure S6 (SI) that the glass-transition temperatures of polymers increase with polymerization degree (n). The inset in Figure S6 (SI) displays n/Tg as a function of n, which implies that the relationship between Tg and n satisfies eq 2 very well, which may be related to the smaller molecular weights of our selected systems.18 According to eq 2 and Figure S6 (SI), we obtain Kg and Tg,∞ of 1134.19 K−1 and 458.72 K, respectively. Figure S7 (SI) demonstrates that there is a linear relationship between the melting temperatures and glass-transition temperatures for some selected PEGDME systems, which is consistent with the result predicted by van Krevelen.20 To examine the reliability of simulated results, we experimentally measure the melting and glass-transition temperatures for PEGDME1000 and PEGDME2000, respectively, in terms of differential

Figure 2. Plots of nonbond potential energy versus temperature for PEGDME polymers with different polymerization degree (n). The nonbond potential energies are shifted up by 0.2, 0.4, 0.6, 0.8, and 1.0 kcal/mol for polymers with n = 11, 15, 23, 45, and 67, respectively. 1719

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Figure 3. Temperature dependence of specific volume (ν) for PEGDME polymers with different polymerization degree (n).

scanning calorimetry (DSC) experiments. Figure 4 reveals the correlation of simulated values (Tg and Tm) with experimental ones (Tg and Tm). The good linear relationship in Figure 4 confirms the reliability of simulated results.

Figure 5. Temperature dependence of thermodynamical quantities (ΔH, TΔS, and ΔG) between amorphous and crystalline PEGDME polymers with different polymerization degree (n = 23, 45, and 67).

TΔS term (ΔG = ΔH − TΔS). It is surprising to find that for PEGDME2000 the entropy changes increase rapidly with temperature, leading to its ΔG values being considerably more negative, as shown in Figure 5 and Figure S9 (SI). It reveals that the main thermodynamic driving force for stability of the amorphous PEGDME2000 is its higher configurational entropy. The results of Figure 5 are in qualitatively agreement with the experiment results10 of Sadowski et al. At first sight, the amorphous PEGDME3000 with larger polymerization degree should have larger configuration number and entropy changes than PEGDME2000. However, as shown in Figure 5, the ΔH−T, ΔS− T, and ΔG−T curves of PEGDME3000 and PEGDME1000 exhibit similar features, which can be explained by the following kinetic reasons. To examine the kinetic behaviors of PEGDME polymers with different phases during cooling processes, we analyze the diffusion coefficients, molecular mobility, and viscosity of selected PEGDME systems. Diffusion coefficients can be obtained from the slopes of the mean square displacements (MSDs)18 as follows:

Figure 4. Correlation of calculated phase-transition temperature with experimental value for PEGDME 1000 and PEGDME 2000.

To examine the roles played by the different interaction components during the glass-transition process, we plot some energy components against temperature for the polymers, as in Figure S8 (SI). Soldera21 reported small breaks in the plots of total, intramolecular, and intermolecular potential energies versus temperature in the simulation of the glass transition of PMMA. In our simulations, we find that there are small breaks near Tg in the plots of torsion energy, electrostatic energy, and nonbond energy versus temperature. For other energy components such as bond energy and angle energy, they decrease linearly with decreasing temperature and there are no significant breaks at the glass transition temperature (Tg) in the plots. The above results reveal that the torsional and electrostatic interactions play roles in the glass-transition process. The enthalphies of amorphous and crystalline PEGDME polymers with different polymerization degree are obtained from current MD simulations. The thermodynamic quantities (ΔH = Hamor − Hcryst, ΔS = Samor − Scryst, and ΔG = Gamor − Gcryst) of the amorphous and crystalline phases are calculated and analyzed from enthalpy data based on the standard thermodynamic relations to reveal the mechanism about the high stability of amorphous PEGDME2000.22 As shown in Figure 5, the enthalpy changes of PEGDME polymers with polymerization degrees of 23, 45, and 67 (PEGDME1000, PEGDME2000, and PEGDME3000) keep constant as temperature increases. For PEGDME1000, the entropy changes increase slowly with temperature. The relatively positive ΔG can be ascribed to the fact that the ΔH term is larger than the

D=

1 d lim ⟨[ri(t + t0) − ri(t0)]⟩ 6 x →∞ dt

(3)

where ri(t) is the position of the center-of-mass (CM) of the PEGDME chain. D is the self-diffusion coefficient, and t is the time. The brackets denote an ensemble average. Relaxation time τ can be obtained based on the following equation18

τ=

⟨R e2⟩ 6D

(4)



represents the mean-square end-to-end distance for polymer chains. It has been known that viscosity η and self-

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Figure 6. Temperature dependence of kinetic data for PEGDME polymers with different polymerization degree (n = 7, 11, 15, 23, 45, 67) during cooling process. (a) D−T, (b) τ−1−T, and (c) η−T.

diffusion D are closely related by the Stokes−Einstein relationship,22−24 that is

ηD = k/6σ T

In summary, melting and freezing behaviors of PEGDME polymers with different polymerization degree are explored and investigated based on MD simulations. The structure and aggregate state of polymers are characterized by bond length, bond angle, dihedral, end-to-end distributions, and global orientational order parameter P2. The good linear relationship between the simulated melting (and glass-transition) temperatures of the polymers and experimental values confirms the reliability of the simulated results. Results reveal that the amorphous PEGDME2000 has relatively high stability based on thermodynamic and kinetic analyses, which is in agreement with the experimental results by Sadowski et al. The high stability of amorphous PEGDME 2000 can be attributed to large configurational entropy and relatively low molecular mobility. The configurational entropies of amorphous PEGDME3000 are smaller than those of amorphous PEGDME2000 because the former has relatively larger viscosities. Our method combining the thermodynamic and kinetic driving forces is sufficiently general that it could serve for examining the stability of other potential solid dispersion reagents and new drugs.

(5)

where T is the temperature and k is the Boltzmann constant. In interatomic average distance σ = (Vatom /Navog) 1/3, Vatom represents the atomic volume and Navog accounts for Avogadro’s number. Figure 6a,b demonstrates the diffusion coefficients and molecular mobilities of selected PEGDME systems, respectively, during cooling processes. As shown in Figure 6a, in total, diffusion coefficients of polymer chains become smaller as the polymerization degree increases. The diffusion coefficients of polymer chains decrease rapidly as the temperatures decrease after the glass-transition temperatures and remain constant before the glass-transition temperatures. The molecular mobilities in Figure 6b have similar features. The above results demonstrate that amorphous PEGDME polymers have low diffusion and low molecular mobility. It is worth noting that the relaxation time (τ) constants at Tg − 50 K for amorphous PEGDME1000 and PEGDME2000 are 66.4 and 372.8 ns, respectively. These values reveal that amorphous PEGDME2000 has a lower molecular mobility, which is also favorable to stabilization of amorphous PEGDME2000. Figure 6c illustrates the temperature dependence of viscosity for PEGDME polymers with different polymerization degree. As shown in Figure 6c, the polymers with longer chains have larger viscosities, as expected. Additionally, the viscosities keep constant above glass-transition temperatures. Below glasstransition temperatures, the viscosities of amorphous systems decrease with increasing temperature. Interestingly, the viscosities of amorphous PEGDME3000 rapidly increase as the temperature decreases, which can be used to explain its lower entropy changes than the expected ones within this temperature region.

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ASSOCIATED CONTENT

S Supporting Information *

Details of the MD simulation and structural analyses. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (X.Z.); [email protected] (X.L.). Notes

The authors declare no competing financial interest. 1721

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in An Entangled Polymer Matrix. J. Chem. Phys. 2010, 132, 194902(1− 10). (19) Douglas, R. W.; Ellis, B. Amorphous Materials; WileyInterscience: London, 1972. (20) van Krevelen, D. W.; te Nijenhuis, K. Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions; Elsevier Science: New York, 1976. (21) Soldera, A. Comparison between the Glass Transition Temperatures of the Two PMMA Tacticities: A Molecular Dynamics Simulation Point of View. Macromol. Symp. 1998, 133, 21−32. (22) Atkins, P.; de Paula, J. Atkins’ Physical Chemistry; W. H. Freeman and Company: New York, 2006. (23) Grosse, A. V. Viscosity and Self-Diffusion of Liquid Metals. Science 1964, 145, 50−51. (24) Cahill, J. A.; Grosse, A. V. Viscosity and Self-Diffusion of Liquid Thallium from Its Melting Point to About 1300 K. J. Phys. Chem. 1965, 69, 518−521.

ACKNOWLEDGMENTS We thank Professor Sadowski for her help in DSC experiments on PEGDME polymers and her valuable comments. This work is supported by grants from the National Science Foundation of China (nos. 21276122, 21136001, and 20876073) and State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing University of Technology of China (no. ZK201212).

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