Enthalpy-driven micellization of oligocarbonate-fluorene end-functionalized Poly(ethylene glycol)

Abstract

A fluorescent pyrene probe method was applied to measure the critical micelle concentration (CMC) of oligocarbonate-fluorene end-functionalized poly(ethylene glycol) (F_mE₄₄₅F_m) triblock copolymers in water. The CMC decreases with lower temperature and higher values of the hydrophobic block length, m. When analyzed by a closed-assembly micelle model, the estimated energetic parameters find a negative ΔH°_mic and small positive ΔS°_mic suggestive of enthalpy-driven micellization, which differs from entropy-driven oxyethylene/oxybutylene triblock copolymers and octaethylene glycol-n-alkyl ethers. The enthalpy-driven micellization of F_mE₄₄₅F_m may result from the limited hydration of individual hydrophobic F blocks that leads to few hydrogen-bonded waters released during F block association. The π-π stacking oligocarbonate-fluorene system also observed enthalpy-entropy compensation when compared to a series of published data on diblock and triblock copolymer systems. An anomalously low partition equilibrium constant for m = 15.3 implies a tightly-packed core that excludes pyrene intercalation into the fluorene core. This is discussed along with the possible limited applicability to estimate the CMC and potential model drug molecule insertions into the intercalated micelle core.

1. Introduction

Polymeric micelles that self-assemble from amphiphilic block copolymers can serve as carriers in delivery applications [1–3]. The critical micelle concentration (CMC) determines how stable the micelles are against dilution under in vivo circulation. The CMC is important for nanoparticles to exploit the enhanced permeability and retention (EPR) effect in tumor tissues for anticancer drug delivery since long in vivo circulation times are required to achieve an effective targeting.

The CMC depends on the insoluble block length and temperature. Astafieva and Eisenberg et al. [4] showed that for polystyrene-b-poly(tert-butyl acrylate), log(CMC) decreases with an increase in the insoluble polystyrene block length. While in the study of Liu and Chu et al. [5], log(CMC) has a linear dependence on the insoluble oxybutylene block length for oxyethylene/oxybutylene (B_mE_nB_m) triblock copolymers. A similar linear dependence of log(CMC) on insoluble block length was observed in Pluronics [6]. As for its temperature dependence, it is well known that the CMC decreases with increasing temperature for Pluronics [7,8]. A contrary dependence of CMC on temperature was observed for polystyrene-b-poly(ethylene/propylene) (PStPEp) and polystyrene-b-poly(ethylene/butylene)-b-polystyrene (SEBS) block copolymer in decane [9] and n-octane [10], respectively. Moreover, it is found that for n-dodecyl polyoxyethylene glycol monoether (C₁₂H₂₅O(C₂H₄O)_nH), CMC initially decreases to a minimum value and then increases as system temperature increases [11].

Based on the temperature dependence of the CMC, the standard enthalpy and entropy change of micellization, ΔH°_mic and ΔS°_mic, respectively, may be estimated [9,12]. The standard free energy change ΔG°_mic of micellization can be derived from the CMC after applying a closed association model [9,12]. These energetic parameters are governed by molecular changes such as chain conformation and interfacial packing, aggregation number, and water hydration extents as a function of temperature. Such changes are related to the thermodynamic stability of micelles in aqueous solution. Accordingly, many studies have focused on this topic. Meguro et al. [13] reported that the positive ΔH°_mic became smaller with higher hydrophobic group content, and the hydrophobic group is an important driving force for micelle formation of octaethylene glycol-n-alkyl ethers (C_mE₈) in aqueous solution. Similar work by Liu et al. [5] observed a positive ΔH°_mic for oxyethylene/oxybutylene (B_mE_nB_m) that decreased with increasing number of hydrophobic oxybutylene units. Bohorquez et al. [14] showed a discontinuity for micellization of Pluronic F127 (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), E_nP_mE_n). They attributed this discontinuity to changes in the aggregation number and/or progressive entanglements between PEO chains. Tsui et al. [15] found a maximum in ΔH°_mic as a function of temperature in a series of Pluronics. Recently, Hoarfrost and Lodge [12] investigated the effect of solvent quality on the critical micelle temperature (CMT) of poly(ethylene oxide-b-n-butyl methacrylate) (PEO-b-PnBMA) in mixtures of ionic liquids. They concluded that ΔH°_mic and ΔS°_mic calculated from the CMT do not vary with solvent quality.

We notice that all the values of ΔH°_mic reported in the above-mentioned studies are positive. In this case, to accomplish the micellization process, ΔS°_mic must be positive to make the overall ΔG°_mic negative through ΔG°_mic = ΔH°_mic - TΔS°_mic. A positive ΔH°_mic indicates the micellization process is entropy driven. The hydrophobic interaction is often viewed as entropic since the binding strength increases with increasing temperature where the effect is attributed to the dehydration of the molecules by water. This is true when the hydrophobic groups are individually hydrated because the hydrophobic hydration reduces the solvent configurational entropy and the release of hydrogen-bonded water during micellization becomes entropically favorable [16]. However, if individual hydrophobic groups are partially or completely dehydrated, Setny et al. suggest that ligand-receptor type associations can be driven by enthalpy [17]. Price and coworkers [9,18] reported that the micellization of polystyrene-b-poly(ethylene/propylene) (PStPEp) block copolymer in organic solvent of decane is enthalpy driven. Recently, Paul et al. [19] showed that the complex formation between bile salts and β-cyclodextrins is enthalpy dominant.

The self-assembly of oligocarbonate-fluorene end-functionalized poly(ethylene glycol) triblock copolymers F_mE_nF_m (Scheme 1) in aqueous solution are analyzed within the thermodynamic framework of micellization. Previous work [20–22] showed the structural aspects of the F_mE_nF_m self-assembly into micelles, but not the temperature effect on the CMC. Here, the pyrene I₃₃₈/I₃₃₃ ratio method was applied to determine the CMC dependence on temperature and hydrophobic block length, m. The energetic parameters are estimated and compared to related polymer systems to provide insights into the driving force of copolymer self-assembly. The equilibrium partition coefficient of pyrene was also estimated. This mimics method used to characterize drug molecules, since F_mE_nF_m could serve as a drug carrier through the electroactive nature of fluorene groups and the biodegradable polycarbonate platform [23]. The results are discussed in relation to the potential application of F_mE_nF_m micelles as nano-carriers.

Scheme 1.

Chemical structure of F_mE_nF_m triblock copolymer.

2. Materials and methods²

F_mE_nF_m triblock copolymer was synthesized as reported in previous studies [21,23]. By varying the feed ratio of spiro[fluorene-9,5’- [1,3]-dioxan]-2′-one (monomer) to that of PEG diol macro-initiator (Sigma-Aldrich, product number 95172 LOT BCBF2828V), a series of polymers were obtained via ring opening polymerization in the presence of 1,8-Diazabicyclo[5.4.0]undec-7-ene (DBU) as the catalyst. As shown in Scheme 1, E represents the middle poly(ethylene glycol), and F is the symmetric substituted oligocarbonate-fluorene group with degree of polymerizations n and m, respectively. These polymers, with the hydrophilic block length n = 445 (based on certificate of analysis), and the hydrophobic block length m = 34.8, 15.3, 5.6, 2, and 1.2 (determined from ¹H NMR spectroscopy in CDCl₃ by comparing the integral values of protons corresponding to PEG to that of oligocarbonate-fluorene segments), are named as F_34.8E₄₄₅F_34.8, F_15.3E₄₄₅F_15.3, F_5.6E₄₄₅F_5.6, F₂E₄₄₅F₂, and F_1.2E₄₄₅F_1.2, respectively, with number-average relative molar mass (M_n) [22] in Table 1. The selected solvent used in this study is 18 MΩ cm resistivity water. Pyrene (puriss. p.a., for fluorescence, ≥ 99.0% (GC), Sigma-Aldrich), inhibitor-free tetrahydrofuran (THF, Sigma-Aldrich), and acetone (Fisher Chemical) were used as received.

Table 1.

Energetic parameters of F_mE₄₄₅F_m calculated^⊥ by Eq. (1).

Polymer	${\mathit{M}}_{\mathbf{\text{n}}}^{\mathbf{\text{a}}}\hspace{0.17em}\mathbf{[}\mathbf{\text{kg}}\mathbf{/}\mathbf{\text{mol}}\mathbf{]}$	${\mathit{Ð}}_{\mathbf{\text{M}}}^{\mathbf{\text{b}}}$	ΔH°mic [kJ mol−1]	ΔS°mic [kJ mol−1 K−1]	ΔG°mic at 25 °C [kJ mol−1]
F34.8E445F34.8	37.2	1.55	–	–	–
F15.3E445F15.3	27.3	1.37	−21.3 ± 0.7	0.078 ± 0.004	−44.4 ± 1.2
F5.6E445F5.6	22.4	1.28	−30.3 ± 0.3	0.052 ± 0.002	−45.9 ± 0.5
F2E445F2	20.6	1.23	−22.6 ± 2.0	0.066 ± 0.012	−42.3 ± 3.5
F1.2E445F1.2	20.2	1.22	−21.0 ± 0.50	062 ± 0.003	−39.5 ± 1.0

^⊥Uncertainties (error bars) were estimated by one standard deviation of the linear regression fit coefficients.

^aBased on ¹H NMR spectroscopy in CDCl₃

^bUncorrected polystyrene equivalent molar-mass dispersity (Ð_M) as determined by size exclusion chromatography in tetrahydrofuran.

2.1. Sample preparation

F₂E₄₄₅F₂ and F_1.2E₄₄₅F_1.2:

F₂E₄₄₅F₂ and F_1.2E₄₄₅F_1.2 block copolymers were dissolved directly in water as clear solutions of 1 mg/mL with stirring. After approximately 24 h, the solutions were diluted to the required concentrations ranging from (5 × 10⁻⁴ to 1.0) mg/mL. 50 μL of 0.01 mg/mL pyrene in acetone was added to a clean glass vial. After acetone was evaporated, 5 mL of polymer solution was added to the vial. The final pyrene concentration in solution is 5 × 10⁻⁷ M (M has been used to represent the SI unit mol/L to conform to the requirement of the Journal). The solution was stirred overnight at room temperature prior to further experiments.

F_34.8E₄₄₅F_34.8, F_15.3E₄₄₅F_15.3 and F_5.6E₄₄₅F_5.6:

An alternate sample preparation method was used in this case, since no fluorescence signal changes was measured as a function of polymer concentration. This reproducible behavior suggests that after the micelles are formed pyrene is excluded from the core. Thus, for F_34.8E₄₄₅F_34.8, F_15.3E₄₄₅F_15.3 and F_5.6E₄₄₅F_5.6, pyrene was added before the micelle forms as follows. A stock solution of 5 × 10⁻⁷ M pyrene in water was prepared by adding known amounts of 0.2 mg/mL pyrene in acetone to an empty flask (1.5 L), following which the acetone was evaporated. Water was added to the flask to give a final pyrene concentration of 5 × 10⁻⁷ M, slightly below the solubility (6 × 10⁻⁷ M) of pyrene in water at 22 °C [24].

50 μL of 0.2 mg/mL pyrene in acetone was added to a clean glass vial. After acetone was evaporated, 2.0 mg of F_15.3E₄₄₅F_15.3 (or F_34.8E₄₄₅F_34.8, F_5.6E₄₄₅F_5.6) and 1 mL of inhibitor-free THF were added to the vial and stirred at room temperature overnight. The clear solution was transferred to a prewashed dialysis membrane with molecular mass cutoff of 3500 Da and dialyzed at room temperature against 5 × 10⁻⁷ M pyrene stock solution (1 L) that was changed after 3, 18 and 21 h. Typically, the final concentration of the polymer solution after dialysis was ≈ 1.7 mg/mL, which could form some sediment. These solutions were vortexed and then serial diluted with 5 × 10⁻⁷ M pyrene stock solution. The final concentration was between (5 × 10⁻⁵ and 0.1) mg/mL.

2.2. Nuclear magnetic resonance (NMR) spectroscopy

The ¹H-NMR spectra of polymers were recorded using a Bruker Avance 400 spectrometer, operated at 400 MHz with the solvent proton signal as the internal reference standard. Polymer samples in D₂O were equilibrated for at least 12 h before data acquisition. Data analysis was performed using TopSpin (version 3.2) software.

2.3. Fluorescence measurement

Excitation fluorescence spectra of the pyrene-containing aqueous polymer solutions were obtained with a JY-Horiba nano-log-3 spectrofluorometer, using an emission wavelength of 390 nm and excitation wavelength range (280–380) nm. A Teflon-stoppered quartz cuvette of 10 mm path length was used. All spectra were run on air-saturated solutions and were accumulated with an integration time of 0.3 s/nm. The temperature range employed was (10–95) °C and at least 5 min was allowed for thermal equilibration. The spectrum at each temperature was an average of 5 scans.

3. Results and discussion

3.1. CMC determination by I₃₃₈/I₃₃₃ ratio

Pyrene is a fluorescent hydrophobic probe with low water solubility [24]. The fluorescence spectrum of pyrene is sensitive to the hydrophilic and hydrophobic environment. At polymer concentrations below the CMC, the environment of pyrene molecules is hydrophilic. As micelles form, near the CMC, pyrene partitions to the interior of the hydrophobic core. Fig. 1a displays a typical excitation spectrum of pyrene in F₂E₄₄₅F₂ aqueous solution at various polymer concentrations.

Fig. 1.

a. A typical excitation spectrum of pyrene in polymer concentration range (5 × 10⁻⁴ to 1.0) mg/mL. b. Plot of the intensity ratio I₃₃₈/I₃₃₃ versus log c for F₂E₄₄₅F₂ at 25 °C. The solid line represents the fit by a Boltzmann-type sigmoid [25].

A shift of the (0, 0) band of pyrene was observed from (333–338) nm with increasing polymer concentration, indicating the transfer of pyrene from a hydrophilic environment to a hydrophobic micellar core [24,26]. The intensity ratio of I₃₃₈/I₃₃₃ increases abruptly above the CMC. As shown in Fig. 1b, the plot of I₃₃₈/I₃₃₃ versus log c is flat at the low polymer concentration extreme and sigmoidal in the crossover region. Herein, CMC was determined using the approach outlined by Aguiar et al. [25] by fitting the plot to a Boltzmann-type sigmoid: $F=\frac{F_{\max }-F_{\min }}{1+e^{(x-x_0)/\Delta x}}+F_{\min }$, where F = I₃₃₈/I₃₃₃, x = log c. The fit parameters are F_max, F_min, x_o and Δx, and CMCs are calculated through the relation, log(CMC) = x_o + 2Δx. Our approach was to use a global fitting method within the Igor Pro software to simultaneously fit the data sets with a common F_max for each polymer at varied temperatures, as represented in Fig. 2. Data fits are made by a weighted least-squares minimization and the uncertainty (error bars) are estimated by one standard deviation of the fit parameter.

Fig. 2.

Plots of the intensity ratio I₃₃₈/I₃₃₃ versus log c for F_mE₄₄₅F_m in the temperature range (10–95) °C. The interval is 5 °C. CMC was determined by fitting the plots to a Boltzmann-type sigmoid. The solid lines are fit curves.

In a new system, the issue of fluorescence quenching should be considered. Fig. 3a shows that with a pyrene concentration of 5.0 × 10⁻⁷ M as the F_15.3E₄₄₅F_15.3 polymer concentration increased, the total fluorescence intensity upon excitation at 333 nm increases at 25 °C. If static quenching occurred, the fluorescence intensity would decrease. All polymers in the m series exhibited similar emission spectra shown in Fig. 3a. Similarly, with an emission wavelength of 390 nm, the excitation spectra of Fig. 1a show of no signs of quenching. Such behavior are consistent with the block copolymer micelles [4,24]. The temperature dependence for the excitation spectra of the highest polymer concentration is shown in Fig. 3b, where the shift in the vibronic peaks occur. The decrease in intensity is not due to quenching, but quantum efficiency, since the polymer concentration is fixed. Finally, all samples were performed in the same air-saturated environment, such that background O₂-fluorescence quenching would be identical.

Fig. 3.

a. Emission spectrum of pyrene within an F_15.3E₄₄₅F_15.3 concentration range (4.88 × 10⁻⁵ to 1.25 × 10⁻²) mg/mL at 25 °C. b. Temperature dependence of the excitation spectrum for fixed F_15.3E₄₄₅F_15.3 concentration.

3.2. Effect on CMC of hydrophobic block length m

The natural logarithmic CMC values at 25 °C versus the hydrophobic block length are shown in Fig. 4. As m increases, one expects the CMC to decrease as also observed by oligocarbonate-cholesteryl PEG triblock polymers [27]. The CMC value of m = 15.3 is attributed to an anomalous partitioning of pyrene into the micelle that will be discussed later along with m = 34.8 which did not give rise to the pyrene fluorescence shift at 25 °C and therefore not reported. As shown in Fig. 4, CMC values determined by pyrene fluorescence (FL) and static light scattering (SLS) at 25 °C are in quantitative agreement with each other despite the sensitivity differences between FL [6,8,24,26] and SLS [22]. For alkylene surfactants, ΔG°_mic is proportional to the number of methylene groups (m) and generally follows [28] log(CMC) ~ m. However, ΔG°_mic of a block copolymer is typically not proportional to the hydrophobic block length. Marko et al. predicted log(CMC) ~ m^2/3 for charged diblock copolymers [29]. A relationship of ln(CMC) ~ m^1/3 was provided by Gao et al. for neutral block copolymers [30]. In our previous study [22], ln(CMC)~ m^{0.47 ± 0.08} was found for F_mE₄₄₅F_m based on SLS data, which falls between limits of m^1/3 and m^2/3. As shown in Fig. 4, it is not possible to distinguish the scaling due to the CMC value of m = 15.3.

Fig. 4.

ln(CMC) of F_mE₄₄₅F_m as a function of the hydrophobic block length m at 25 °C from pyrene fluorescence (FL □) and static light scattering (SLS ■) from Ref. [22]. Literature CMC data provided by the legend at 25 °C unless otherwise indicated:, B₅E₉₁B_5, B₆E₄₆B_6, B₁₀E₂₇₁B₁₀, and B₁₂E₂₆₀B₁₂ from Ref. [5]; B₄E₄₀B_4, B₅E₃₅B₅ and B₇E₄₀B₇ at 20 °C from Ref. [32]; C₁₆PEOC₁₆ from Ref. [33]; (Inset) Scaling of abscissa by the Flory-Huggins interaction parameter and additional scaling constant α = 7.1 for the F_mE₄₄₅F_m data.

The supporting literature from systematic studies of B_mE_nB_m and C₁₆ alkylene end-capped poly(ethylene oxide), (C₁₆PEOC₁₆) in water are shown in Fig. 4. The data are superimposed by using the estimated Flory-Huggins interaction parameter (χ) between the insoluble block with water. χ(F_m-water) = 1.06, χ(C₁₆ alkylene-water) = 1.20, and χ(B_m-water) = 0.81 were estimated by the group contribution method [31]. An additional factor of α = 7.1 was required to scale the F_mE₄₄₅F_m data to overlap the B_mE_nB_m series.

3.3. Self-assembly transition line

Fig. 5 shows that the CMC of F_mE₄₄₅F_m increases with temperature. The increment of CMC is a direct consequence of the decrease in binding strength of F blocks in water, which agrees with the increment of fluorene solubility in water with temperature [34]. The temperature dependence of the CMC of F_mE₄₄₅F_m is opposite to that of Pluronics (E_nP_mE_n) that display a CMC decreasing with increasing temperature [6,8]. Investigating this opposite behavior between F_mE₄₄₅F_m and Pluronics could improve the understanding of the driving force of copolymer self-assembly with supramolecular assembly functionality. For Pluronics, the hydrophobic P block, poly(propylene oxide), is highly hydrated at low temperatures even in the hydrophobic micellar core. As reported by Yang et al. [35], for Pluronic L64 at 37 °C the poly(propylene oxide) micelle core contained 40 % of water by volume and this number decreased to 5 % at 55 °C. The loss of water in the micellar core indicates the dehydration of the P block in water at high temperature. The release of hydrogen-bonded water at high temperature results in a significant increase of hydrophobicity, and consequently, CMC decreases. In contrast, the hydration level of associated F blocks in F_mE₄₄₅F_m is low because of the π-π stacking of the fluorene groups that do not display hydrogen-bond donor or acceptor groups to free water. In contrast to C_mE_n [11,36], F_mE₄₄₅F_m does not show a minimum CMC in temperature-CMC plot within the temperature range available.

Fig. 5.

Experimental temperature-CMC plots of self-asssmbly transition of F_mE₄₄₅F_m triblock copolymer. The solid lines are guides for the eye.

Comparison of the experimental trends to a simple polymer micelle model provides insight into the temperature dependence of the CMC. Spherical micelle formation can be estimated by Ref. [37], $CMC=e^{-4\pi a^2\gamma /kT}$, where a is the length per monomer of hydrophobic block and g is the interfacial tension between hydrophobic core and solvent. Raspaud et al. suggest a²γ may be estimated by ln $\ln \left(\frac{1}{\phi s}\right)=a^2(\gamma /kT){(3{(4\pi )}^{1/2}m)}^{2/3}$ where ϕ_s is the solubility limit at the same temperature of a homopolymer having the same degree of polymerization (m) as the insoluble block polymer [38]. While the solubility limit and interfacial tension with water of the hydrophobic fluorene-carbonate monomer is not known, the fluorene solubility is tabulated [39]. In fact, the aqueous solubility of fluorene increases with increasing temperature, this leads to a lower interfacial tension that shifts the CMC to higher concentrations, in correct trend with all the experimental data in Fig. 5. Attempts to use the fluorene solubility shows these trends with a degree of polymerization dependence, however, the solubility of the carbonate-fluorene monomer most likely is higher than pure fluorene which has a substantial effect on the magnitude of the estimated CMC.

3.4. Energetic parameters of ΔG°_mic, ΔH°_mic, and ΔS°_mic

The energetic parameters of micelle formation per mole of copolymer chains were estimated by a closed association model [9,12].

$$\begin{gathered} \Delta G_{mic}^{\circ }=RT\ln (CMC); \\ \Delta H_{mic}^{\circ }=-R{T}^2{\left[\frac{d\ln (CMC)}{dT}\right]}_P; \\ \Delta S_{mic}^{\circ }=(\Delta H_{mic}^{\circ }-\Delta G_{mic}^{\circ })/T, \end{gathered}$$ (1)

where CMC is in mole fraction of polymer in aqueous solution obtained from the concentration in mg/mL by use of the polymer molecular mass (Table 1), water mass density and molecular mass. The ΔH°_mic may be estimated from the plot of ln(CMC) versus reciprocal T, as shown in Fig. 6. The estimated energetic parameters: ΔG°_mic, ΔH°_mic, and ΔS°_mic are shown in Table 1.

Fig. 6.

The plots of ln(CMC), in mole fraction of polymer, versus reciprocal T for F_mE₄₄₅F_m, used for the determination of DH°mic in terms of the closed association model. The solid lines are linear regression fits to the data with uncertainties (error bars) estimated by results of the Boltzmann sigmoidal method that determines the CMC.

The negative values of ΔG°_mic indicates that micelles formed by F_mE₄₄₅F_m are stable at room temperature. The negative ΔH°_mic shown in Table 1 indicates that the transfer of polymer chains from solution to micelles is enthalpically favorable. Note that ΔG°_mic < 0 in Table 1 is mainly due to enthalpy effects with small positive ΔS°_mic. The range of values of ΔS°_mic for F_mE₄₄₅F_m, (0.052–0.078) kJ·mol⁻¹·K⁻¹, are an order of magnitude lower than the reported values of Pluronics, (0.638–1.244) kJ·mol⁻¹·K⁻¹ [6]. This observation implies that the micellization of F_mE₄₄₅F_m is predominantly enthalpy driven with small entropic contribution to the total free energy change of ΔG°_mic. F_15.3E₄₄₅F_15.3 exhibits a change in the trends with m. A low pyrene partition into the micellar core at m = 15.3 is speculated. A molecular model would be necessary to further discriminate the details of these trends.

A comment is necessary on the effect of chain architecture. One can compare the free energy of placing a hydrophobic block into solvent to that of forming a loop (flower-like micelle chain conformation) [40]. In this case, the role of chain architecture, such as ABA versus BAB, is sensitive to the molecular mass of the blocks and the Flory-Huggins interaction parameter (χ) between segment and solvent. The enthalpic origin for the free energy of placing m hydrophobic (A) segments into solution (s) is kTχ_AS m. While the entropic origin for the free energy of forming a loop with n segments of water-soluble B block is kTln(πχ_BS n)/3. Using estimates for the interaction parameters (χ_AS = 1.06 and χ_BS = 0.63) we find that the entropic penalty for loop formation of n = 445 segments equals the enthalpy of placing hydrophobic segments into water to be m = 2.1. This estimate suggests loop formation is the preferred conformation for end block segments greater than 2.1. Chain architectures that lead to more loops may exhibit such an entropy penalty to lower the positive ΔS upon micellization as observed for F_mE₄₄₅F_m and the difference between E_nP_mE_n and P_mE_nP_m (see Table 2). Such estimates, however, do not consider the important contributions of solvation.

Table 2.

Comparison of energetic parameters of F_mE₄₄₅F_m to selected literature.

	Polymer	Solvent	Hydrophobic units, m	Hydrophilic units, n	ΔH°mic [kJ mol−1]	ΔS°mic [kJ mol−1 K−1]	ΔG°mic at 25 °C [kJ mol−1]
FmEnFm	F15.3E445F15.3	Water	15.3	445	−21.3	0.078	−44.4
	F5.6E445F5.6	Water	5.6	445	−30.3	0.052	−45.9
	F2E445F2	Water	2.0	445	−22.6	0.066	−42.3
	F1.2E445F1.2	Water	1.2	445	−21.0	0.062	−39.5
PmEnPm	[41]10R5	Water	8	22	115	0.419	−9.9
	[7]17R4	Water	14	24	115	0.40	−4.3
a EnPmEn [6]	L64	Water	27	15	230	0.835	−24.5
	P65	Water	25	22	182	0.671	−25.3
	F68	Water	23	80	215	0.756	−28.8
	P84	Water	39	22	211	0.784	−25.2
	P85	Water	34	30	229	0.842	−25.5
	F88	Water	31	109	169	0.638	−28.5
	P103	Water	55	20	339	1.244	−24.8
	P104	Water	54	31	296	1.092	−25.4
	P105	Water	48	42	331	1.212	−25.6
	F108	Water	40	139	266	0.975	−28.4
	P123	Water	63	23	329	1.223	−24.9
	F127	Water	53	108	253	0.944	−27.5
CmEn [13]	C10E8	Water	10	8	18	0.152	−27
	C11E8	Water	11	8	17	0.156	−30
	C12E8	Water	12	8	15	0.164	−33.6
	C13E8	Water	13	8	14	0.167	−36
	C14E8	Water	14	8	13	0.172	−38.7
	C15E8	Water	15	8	11	0.176	−41.1
			Solvophobic Mw kg/mol (m)	Solvophilic Mw kg/mol (n)
SEBS [10] a Sm(EB)Sm	S88EBS88	n-octane	9.1 (88)	42.5	−36.8	0.0328	−27.0
PStPEp [18] a	S135EBS135	n-octane	14 (135)	59.4	−41.9	0.0359	−31.2
	S478EP1414	decane	49.8 (478)	168 (1414)	−181	0.391	−43.0
Sm(EP)n	S358EP877	decane	37.3 (358)	106 (877)	−141	0.283	−41.5
	S302EP1154	decane	31.5 (302)	130 (1154)	−103	0.173	−41.7

^aThe block length m and n are estimated from the published relative mass-average molecular mass (M_w) of each block.

3.5. Comparison of F_mE₄₄₅F_m to prior study: nature of hydrophobic self-assembly

Herein, we compare F_mE₄₄₅F_m to E_nP_mE_n, C_mE₈, P_mE_nP_m, SEBS, and PStPEp to understand underlying driving forces for hydrophobic self-assembly. The experimental data are summarized in Table 2 and the available ΔH°_mic and ΔS°_mic are plotted in Fig. 7.

Fig. 7.

The plot of ΔH°_mic versus ΔS°_mic of E_nP_mE_n [6], C_mE₈ [13], PStPEp [18] and F_mE₄₄₅F_m. The dashed line indicates the linear fit of ΔH°_mic versus $\Delta {{\rm H}}_{\text{mic}}^{\circ }=\Delta {{\rm H}}_{\text{mic}}^{\circ }+T_c\Delta S_{\text{mic}}^{\circ }$.

When ΔH°_mic and ΔS°_mic are both negative, as shown in Fig. 7, the enthalpy driven micellization occurs only below a “ceiling temperature” [42] where ΔH°_mic is more negative than TΔS°_mic. If ΔH°_mic and ΔS°_mic are both positive, to make ΔG°_mic negative, micellization occurs above a “floor temperature” [42] where ΔH°_mic is smaller than TΔS°_mic, namely, micellization is entropy driven. In Fig. 7, it is observed that ΔH°_mic and ΔS°_mic of E_nP_mE_n and P_mE_nP_m are both positive, indicating the micellization in water is entropy driven. The release of hydrogen-bonded water from the hydrophobic P block during micellization is entropically favorable. Seemingly, micellization of C_mE₈ is also entropy driven. However, after separating ΔG°_mic into contributions from the hydrophobic (ΔG°_mic(h)) and hydrophilic (ΔG°_mic(-w)) groups [13], the both positive ΔH°_mic(-w) and ΔS°_mic(-w) of C_mE₈(-w) in Fig. 7 clearly indicate that transferring a hydrophilic group from unimer state to micellar state is entropically favorable, while the negative ΔH°_mic(h) of C_mE₈(h) suggests that micellization of C_mE₈ induced by hydrophobicity is predominantly enthalpy driven. This observation confirms that E_nP_mE_n and P_mE_nP_m is entropy driven because of the entropically favorable dehydration of P block during micelle formation. The net positive ΔH°_mic, suggests that the hydrophilic group association overwhelms the favorable negative enthalpy change from hydrophobicity. While the net positive ΔS°_mic suggests the entropy gain from the release of hydrogen-bonded water upon micelle formation overcomes the configurational entropy loss caused by transferring the hydrophobic group from aqueous to the micellar phase. Based on this, ΔH°_mic is negative for F_mE₄₄₅F_m (Fig. 7) because of the low hydration level of individual F blocks in water, thus the hydrophobicity of F blocks and π-π stacking effects dominate the enthalpy change. The group contribution estimate for χ between the aliphatic carbonate-fluorene group in water supports the low solubility. The low hydration level of individual F blocks results in a small entropic contribution due to the release of few hydrogen-bonded water upon micelle formation. Additionally, we observe that ΔH°_mic and ΔS°_mic of PStPEp and SEBS in Fig. 7 are both negative. This is suggestive of an enthalpy driven micellization for PStPEp and SEBS in organic solvents (no hydrogen bond effects). This observation confirms that solvation entropy associated with the hydrogen-bond network plays an important role in hydrophobic self-assembly of F_mE₄₄₅F_m.

It is observed by Fig. 7 that the micellization for the systems shown exhibit an enthalpy-entropy compensation relationship [11,15,36,43–46] of $\Delta {{\rm H}}_{mic}^{\circ }=\Delta {{\rm H}}_{mic}^{*}+T_c\Delta S_{mic}^{\circ }$ with common ΔH*_mic, (−39 ± 2) kJ·mol⁻¹, and T_c, (313 ± 3) Κ. The intercept ΔH*_mic is an index of the solute-solute interaction, while the slope T_c measures the solute-solvent interaction. The universal behavior in Fig. 7 indicates that the hydrophobic interaction for self-assembly, though being either entropy or enthalpy driven, has the same physical feature, i.e, the solvent-solute interaction is significantly less than solute-solute interaction. Depending on temperature, the self-assembly would shift along the enthalpy-entropy compensation line, leading to a transition between entropy and enthalpy driven. It has been reported that in protein folding, the hydrophobic interaction changes from being entropy driven at low temperature to being enthalpy driven at high temperature [47]. This is reminiscent of the minimum CMC in CMC-temperature curve of C_mE_n reported previously [11,36]. The non-monotonic temperature dependence of the CMC may result from the temperature dependence of solvation entropy.

3.6. Partition equilibrium of pyrene molecules

The enthalpy-entropy compensation concept also appears in drug receptor binding [48]. This drug partitioning can be estimated by the pyrene fluorescence method. The partition coefficient P, determines the fraction of drugs encapsulated by the micellar phase, and therefore characterizes the drug-encapsulation stability. Here, the fluorescent probe of pyrene may be considered as a model intercalating probe characterized by the partition equilibrium between aqueous solution of F_mE₄₄₅F_m triblock copolymers.

The partition coefficient P is given by Ref. [8] $P=\frac{{\left|\text{Py}\right|}_{\text{m}}}{{\left|\text{Py}\right|}_{\text{w}}}$ [Py]_m and [Py]_w are the local pyrene concentration in micellar and aqueous phase, respectively. Wilhelm and Winnik et al. [24] provided a method to calculate P and partition equilibrium constant K_v by fluorescence experiments: $P=\frac{{\left|\text{Py}\right|}_{\text{m}}}{{\left|\text{Py}\right|}_{\text{w}}}=\frac{F-F_{\min }}{F_{\max }-F}$, $P=\frac{{\left|\text{Py}\right|}_{\text{m}}}{{\left|\text{Py}\right|}_{\text{w}}}=\frac{K_{\text{v}}{W}_{\text{F}}C}{1000{\rho }_{\text{F}}}$ where W_F is the mass fraction of F groups in F_mE₄₄₅F_m and ρ_F is the density of micellar core formed by F groups, which we shall assume the bulk value for fluorene (1.202 g/mL). Plots and the linear regression fits of [Py]_m/[Py]_w versus polymer concentration c of F_mE₄₄₅F_m are shown in Fig. 8.

Fig. 8.

Plots of [Py]_m/[Py]_w versus polymer concentration c of F_mE₄₄₅F_m with increasing temperatures from (10–95) °C. The interval is 5 °C. The solid lines represent the fits. The partition equilibrium constant K_v is calculated from the slope of each curve.

The partition equilibrium constant K_v, calculated from the slope of [Py]_m/[Py]_w versus c in Fig. 8, is displayed in Fig. 9. The values of K_v are all on the magnitude of 10⁵, similar to the reported values for the partition of pyrene into polystyrene micellar phase of poly(-styrene-b-ethylene oxide) block copolymer [24]. The magnitude (10⁵) of K_v indicates that the partition of pyrene into micellar phase of F_mE₄₄₅F_m is strongly favorable. In Fig. 9, we observe that K_v decreases with increasing temperature, indicating a gradual decrease in the binding strength between pyrene and micelles. This observation is consistent with our earlier discussion that the hydrophobicity of F blocks decreases with increasing temperature, underlining the increase of CMC at high temperature in Fig. 5. In Fig. 9, we also observe that K_v increases as the hydrophobic block length m increases from 1.2 to 5.6. This trend suggests an incremental increase of hydrophobicity in F_mE₄₄₅F_m favors partition of pyrene into the micellar phase. Similar behavior has been reported for the partition coefficient P of pyrene which increases with the increment of Pluronic hydrophobicity [8]. It is noted that in Fig. 9, K_v of F_15.3E₄₄₅F_15.3 is anomalously low, underlining the anomalous CMC value of F_15.3E₄₄₅F_15.3 in Fig. 4, which most likely results from a tightly-packed core structure of F_15.3E₄₄₅F_15.3 and similarly F_34.8E₄₄₅F_34.8 which did not give rise to a systematic pyrene signal. The K_v of pyrene for the semi-crystalline core of poly(caprolactone-b-_l-lactide), P(CL-LLA), in mPEG-P(CL-LLA) is lower than that of the amorphous core of poly(caprolactone-b-_D,l-lactide), P(CL-DLLA), in mPEG-P(CL-DLLA) [49]. Consequently, the CMC values measured by the pyrene method for polymers with semi-crystalline P(CL-LLA) core were higher than that of the amorphous P(CL-DLLA) core [49]. A similar trend was observed with diblock copolymers of PEG with polylactic acid, where an increased CMC was observed with increased stereoregularity [50]. Moreover, it is known that oligo(-dibenzofulvene) having fluorene as a side chain can form crystals due to the π-π stacking of fluorenes [51]. While our efforts to observe a core glass transition or melting were inconclusive, perhaps due to the low molecular mass of the end groups, calorimetric studies of fluorene-functionalized aliphatic poly(-carbonates) had glass transition temperatures exceeding 100 °C [52]. Based on these observations, we expect that F_15.3E₄₄₅F_15.3 and F_34.8E₄₄₅F_34.8 has a packed core that may exclude the pyrene and consequently reduce the partition equilibrium constant K_v. The refractive index increment was also higher from our previous study and correlates to packing [22]. The phenomenon we observe in Fig. 9 could guide the design of novel polymers with higher drug loading capacity [53].

Fig. 9.

Partition equilibrium constant K_v of F_mE₄₄₅F_m at different temperatures. The solid lines are guides for eyes.

An indirect approach to estimate the accessibility of the fluorene groups is ¹H NMR spectroscopy. NMR spectra were collected on five F_mE₄₄₅F_m samples in D₂O and CDCl₃. Samples in CDCl₃ are completely dissolved, since CDCl₃ is a good solvent for both blocks, while D₂O is a poor solvent for the F blocks. Comparison of the integral values of protons corresponding to PEG block to that of oligocarbonate-fluorene block in D₂O and CDCl₃ could provide insights on fluorene packing. The observed protons integrated over the aromatic region (8.2 ppm–7 ppm) for samples in D₂O normalized by the respective theoretical aromatic protons based on the NMR data in CDCl₃ show that aromatic protons become less solvent accessible with increasing m in Fig. 10. This correlates to our primary conclusion that at higher m the local packing of fluorene groups may exclude pyrene from the micelle core. By combining this new qualitative data and the partition coefficient results, we suggest a cross-over value of m, between m = 5.6 and 15.3, where the pyrene method becomes less reliable due to the more effective packing of the fluorene groups.

Fig. 10.

Ratio of observed to theoretical aromatic protons from the fluorene groups integrated over 8.2 ppm–7.0 ppm, from solution-state ¹H-NMR in D₂O. The reduction in the observed aromatic protons are consistent with less solvent-accessibility with increasing m.

4. Conclusions

The temperature and hydrophobic block length dependence of the CMC for F_mE₄₄₅F_m follows the thermodynamics of self-assembly when analyzed by a closed association model. The lower CMC at larger m indicates a tendency for stable micelles under dilution, which is advantageous for in vivo circulation. However, simultaneously, the largest m led to a smaller pyrene probe partition co-efficient. Therefore, a trade-off occurs when designing polymer micelles via self-assembly for encapsulation. This effect is consistent with the trends from semi-crystalline core block copolymers that exclude probe molecules and lead to higher CMC estimates than amorphous cores. The F_mE₄₄₅F_m CMC increases with increasing temperature due to the increased solubility of the fluorene groups with temperature, which is opposite to Pluronic micelles. The origin of this behavior can also be captured by a self-assembly model with a temperature dependent interfacial tension. A negative ΔH°_mic estimated for F_mE₄₄₅F_m indicates an enthalpy driven micellization, which differs from the entropy-driven polymers of E_nP_mE_n, P_mE_nP_m, and C_mE₈. This difference was attributed to the minor contribution of hydrogen-bonded water to fluorene during micelle formation.