Viscoelastic Response of Double Hydrophilic Block Copolymers for Drug Delivery Applications

1. Introduction

Bottlebrush polymers, characterized by densely grafted macromolecular architecture, have attracted considerable attention owing to their highly tunable physical and chemical properties, which depend on side chain length, backbone length, and grafting density [1,2,3,4,5,6,7,8]. In comb polymers, side chains act as a solvent, diluting backbone concentration - a phenomenon known as dynamic tube dilution [4,9,10,11]. This effect results in low viscosity and a reduced rubbery plateau. These properties make bottlebrush block copolymers promising for applications in drug delivery, energy storage, nanostructures, catalysis, and 3D printing [12,13,14,15,16,17,18,19,20,21,22,23].

Double hydrophilic block copolymers (DHBCs), composed of two chemically distinct water-soluble blocks, are important in polymer science, pharmacy, biophysics and biochemistry [24,25,26,27]. They offer an alternative option to traditional amphiphilic block copolymers and self-assemble in aqueous conditions in response to changes in ionic strength, temperature, pH, or complexation with specific (bio)molecules. DHBCs with charged blocks, known as polyelectrolytes, are promising candidates for biomacromolecule delivery via electrostatic complexation [28]. For enhancing water solubility and stability in aqueous media, a neutral block, such as poly(ethylene glycol) or poly(oligo(ethylene glycol) methacrylate) (POEGMA), is used.

Diblock and statistical copolymers consisting of poly[oligo(ethylene glycol) methacrylate] (POEGMA) and poly(vinyl benzyl trimethylammonium chloride) (PVBTMAC) have been successfully synthesized using a reversible addition−fragmentation chain transfer (RAFT) polymerization process [26,27]. Recent research studies have focused on these copolymers’ abilities to form electrostatic complexes with hydrophilic magnetic nanoparticles, short DNA and negatively charged proteins (i.e. insulin) [26,27]. Additionally, the relaxation dynamics and the self-assembly of these DHBCs were investigated under dry conditions [29]. It was evidenced that the weak segregation strength between the two hydrophilic blocks results in homogeneous dynamics that are governed by the interfacial glass transition temperature (T_g^inter) [29]. A detailed study of the viscoelastic response of these DHBCs is missing from the existing literature and such information is of interest for scientists working on these promising DHBCs for biomedical applications. It is worth noting that DHBCs with densely grafted macromolecular architecture are also promising for the design of novel solid polymer electrolytes for battery applications [19,20,22,23].

Herein, block and random DHBCs were studied by means of rheological measurements. We report that the PVBTMAC homopolymer exhibits an elastic-response up to high temperatures, reflecting its strong (i.e. rigid) nature. In the first part, the effect of the VBTMAC block on the zero-shear viscosity, determined by using two empirical models, is presented. In the second part, the rheological data are discussed with respect to classical free volume theories of glass formation. The values of fractional free volume, thermal expansion coefficient, fragility, and apparent activation energy at the glass transition temperature (T_g) are reported and compared with those of the PVBTMAC parent homopolymer.

2. Materials and Methods

2.1. Synthesis

The synthetic procedure and molecular characterization of the studied DHBCs is highlighted in previous studies [26,27]. Specifically, the charged DHBCs with densely grafted macromolecular architecture were prepared by RAFT polymerization, an advantageous method for controlling the molar mass (M_w) and achieving polydispersity values close to unity [30,31]. The chemical structure of the investigated DHBCs is depicted in Figure 1.

2.2. Rheology

Rheological measurements into the linear viscoelastic regime (LVR) can provide quantitative insight into the viscoelastic response of the studied polymeric materials [32]. A MCR-302 twin mode rheometer by Anton Paar was used for the identification of the viscoelastic properties of grafted copolymers under dry conditions. Measurements were made with the environmental test chamber as a function of temperature, by using the heating system (P-PTD200). The samples were prepared on the lower rheometer plate with a diameter of 8 mm. Specifically, the upper plate was brought into contact, and the sample thickness was adjusted accordingly. Typically, the gap between plates ranged between 0.3 mm to 0.6 mm, among the investigated DHBCs. At each temperature the linear viscoelastic region of the copolymers was determined by performing strain sweeps of the complex shear moduli |G*| from 0.01 to 50% (the upper limit varies regarding the state of the material), at ω = 10 rad·s^-1, as shown in Figure S1. Subsequently, isothermal frequency sweeps in an angular frequency range of 0.1 < ω < 100 rad·s^-1 were carried out in temperature steps of 10 K, by employing the extracted strain amplitude of the dynamic strain sweep. Before each isothermal measurement, a thermal stabilization of 20 min was employed to ensure thermal equilibrium. Data collected under the minimum torque of the instrument were excluded. Master curves were constructed by using the principle of time-temperature superposition (tTs). For estimating the zero-shear viscosity, we used an extrapolation procedure for the data that do not reach the Newtonian limit at low frequencies. Empirical models can be utilized to fit the complex viscosity response and extrapolate to low frequencies to estimate the value of zero-shear viscosity, η₀. Specifically, the Carreau-Yasuda (CY) model is given by the following equation [33,34]:

$${\eta }^{*}\left(\omega \right)={\eta }_0{\left[1+{\left(\lambda \omega \right)}^{\alpha }\right]}^{{\displaystyle \frac{n-1}{\alpha }}}$$

(1)

where, λ is the relaxation time, α indicates the width of the transition region between Newtonian and power-law behavior and n is the power-law index (i.e. a measure of the shear-thinning nature of a polymer melt). All these parameters can be obtained by fitting the measured data. Another empirical model that can be used for fitting the viscosity data is the modified Cross (MC) model, according to [35]:

$${\eta }^{*}\left(\omega \right)={\displaystyle \frac{{\eta }_0}{1+{\left[C_0\omega \right]}^{1-n}}}$$

(2)

where, C₀ and n can be extracted by fitting the data to Equation 2.

3. Results and Discussion

Quantitative insight into the viscoelastic response of the dried DHBCs can be obtained through small amplitude oscillatory shear (SAOS) rheological measurements. The effect of temperature under isochronal conditions (i.e. at a fixed angular frequency of 10 rad·s^-1) on the mechanical properties of the dried copolymers is depicted in Figure S2. The PVBTMAC homopolymer exhibits elastic behavior up to extremely high temperatures, indicating its rigid/strong nature. The temperature dependence of the loss factor verifies the existence of two T_gs, associated with the backbone and side chain vitrification [29]. Regarding the statistical copolymers, at a fixed temperature, they exhibit reduced shear moduli that is attributable to the influence of the soft OEGMA segments. Additionally, the viscoelastic response is governed by T_g^inter, defined at the crossing point of shear storage (G') and loss (G'') moduli, verifying their disordered and well mixed state, as observed by X-ray diffraction [29].

The dynamic frequency sweeps into the linear viscoelastic response under isothermal conditions (i.e. 293 K), for the statistical copolymers with various compositions are shown in Figure 2.

Initially, the dynamic frequency sweep unveils that the PVBTMAC homopolymer exhibits a strong nature and elastic response (G' >> G'' ~ ω⁰). In going to the statistical copolymer containing 40 wt.% VBTMAC, a viscoelastic response, characterized by comparable and frequency-dependent storage (G') and loss (G'') moduli, can be observed. By further decreasing the VBTMAC content to 20 wt.%, a liquid-like response (G' ~ ω² and G'' ~ ω¹) is evident. In the latter copolymer, the complex viscosity (${\eta }^{*}=\sqrt{{G^{\text{'}}}^2+{G^{\text{'}\text{'}}}^2}/\omega$), exhibits a plateau at lower angular frequencies, from which the zero-shear viscosity, η₀ can be extracted. For extracting the zero-shear viscosity, the measured data were fitted/modelled with two different empirical models, as detailed in the experimental section. The fitting parameters are provided in Table 1. In addition, the dynamic frequency data of the statistical copolymers are compared and contrasted with those found at PVBTMAC homopolymer under iso-T_g temperatures (i.e. T_g + 30 K), in Figure S3. The iso-T_g comparison reflects the changes in viscoelastic response from elastic to viscoelastic and liquid response by decreasing the VBTMAC content, quantitatively verifying the observations at ambient temperature.

Concerning the statistical copolymers, the relaxation time, λ, increases by increasing the concentration of VBTMAC glassy blocks. The extracted values of the power law index, n imply a shear-thinning behavior of the copolymer melts, that becomes stronger by increasing VBTMAC content. For the copolymer with 40 wt.% VBTMAC and the PVBTMAC homopolymer, the values of zero-shear viscosity extracted from MC model are slightly higher than the one obtained from CY model.

The effect of block arrangement along the backbone can be discussed with respect to Figure 3 and Table 1, comparing the dynamic frequency sweep data of the sequential and statistical copolymer with a VBTMAC content of 20 wt.%.

The sequential arrangement of VBTMAC glassy blocks yields an elastic-response (G' >> G'' and G', G' ~ ω⁰), compared to the liquid-like response of the statistical copolymer, indicating the presence of larger and continuous bulk-like VBTMAC regions, despite the fact that both specimens are into the disordered state, as evidenced in our previous study [29]. Parenthetically, a reduced change of heat capacity for T_g^inter was evidenced for the sequential copolymer compared to the statistical, verifying the aforementioned observations [29]. The determination of the zero-shear viscosity is challenging and inaccurate for the sequential copolymer, due to its predominantly elastic response, even at elevated temperatures (see Figures S4 and S5), hindering the low-frequency plateau in the viscosity data. To mitigate this challenge, the viscosity data were fitted with the empirical models of Eq.1 and 2, yielding a higher value of zero shear viscosity by approximately 3 orders of magnitude, compared to the corresponding statistical copolymer. This indicates that the block arrangement along the copolymer backbone plays a crucial role in tailoring the viscoelastic response of the studied DHBCs.

The extracted values for zero-shear viscosity are summarized in Figure 4.

The dynamic frequency sweeps for the statistical copolymers are presented at different temperatures in Figure S6, along with the temperature dependence of the extracted power law index. The latter increases by increasing temperature, implying less shear thinning behavior, as evident from the flattening of the viscosity curves.

Detailed information about the viscoelastic response of the studied copolymers can be obtained through the construction of master curves by employing the tTs principle, which involved the horizontal shifting of dynamic frequency sweeps, as shown in Figure 5.

For the copolymer containing 20 wt.% VBTMAC, a well-defined terminal regime (G' ~ ω² and G'' ~ ω) is observed, confirming its liquid- or melt-like behavior. In contrast, the copolymer with 40 wt.% VBTMAC maintains a viscoelastic response even at high temperatures (i.e., low frequencies), highlighting the influence of the glassy VBTMAC segments. As depicted in Figure 5 and Figure S2, the absence of large rubbery plateaus is attributable to the low molar masses and the short side chain lengths, that distinctly reduce the entanglements. Figure 5(b) presents the normalized complex viscosity, adjusted using horizontal shift factors, as a function of normalized angular frequency. This representation of the master curves for the statistical copolymers confirms the viscosity variation with copolymer composition. Simultaneously, the extracted values of power law index, by employing the MC model, indicates that both statistical copolymers display comparable levels of shear thinning behavior. The temperature dependence of the extracted horizontal shift factors is depicted in Figure 6.

The results can now be discussed in terms of classical free volume theories of glass formation [32]. As shown in Figure 6, the extracted shift factors, α_T, were fitted according to the WLF equation [37]:

$$\log {\alpha }_T=-{\displaystyle \frac{{c_1}^r\left(T-T^r\right)}{{c_2}^r\left(T-T^r\right)}}$$

(3)

where, c₁^r and c₂^r are empirical parameters at the reference temperature, that is T_r = 343 K, for the studied DHBCs and PVBTMAC homopolymer. According to the theory, the empirical parameters can be calculated at T_g; c₁^g = c₁^r c₂^r/( c₂^r + T_g - T_r) and c₂^g = c₂^r +T_g - T_r, and then the fractional free volume, f(T_g), and the thermal expansion coefficient of free volume, α_f, can be extracted, according to:

$$f(T_g)={\displaystyle \frac{1}{2.303c_1^g}}$$

(4)

$${\alpha }_f={\displaystyle \frac{f\left(T_g\right)}{c_2^g}}$$

(5)

Furthermore, the fragility or steepness index, m*, and apparent activation energy, E_g can be estimated from [38,39]:

$$m^{*}={\displaystyle \frac{c_1^g{T}_g}{c_2^g}}$$

(6)

$$E_g=2.303R{\displaystyle \frac{c_1^g}{c_2^g}}{T}_g^2$$

(7)

The estimated parameters are summarized in Table 2 and can be discussed with respect to Figure 7 and Figure 8.

The copolymers exhibit slightly increased fractional free volume in relation to the PVBTMAC homopolymer, indicating the effect of the soft OEGMA segments, that further increase the free volume between the segments. These differences in fractional free volumes are primarily correlated to changes in T_g values between the PVBTMAC homopolymer and the statistical copolymers, that are mirrored to the c₁^g parameter. Instead, the c₂^g parameter appears to have a peculiar dependence on the VBTMAC content and distinctly decreases by increasing the VBTMAC content from 20 wt.% to 40 wt.%, yielding slight changes to the thermal expansion coefficient of DHBCs. The latter is in proximity to the one found for the PVBTMAC homopolymer. Importantly, the c₂^g of PVBTMAC is four times larger compared to Polystyrene (PS) [40], thereby reducing fragility values, as discussed below with respect to Figure 8a.

The effect of the VBTMAC composition on the fragility and apparent activation energy are discussed in relation to Figure 8.

Figure 8. (a) Fragility and (b) apparent activation energy as a function of the VBTMAC weight fraction for the copolymers (squares) and their parent blocks (stars). Fragility data from dielectric measurements, taken from ref [29] are also included along with fragility data for PS taken from ref [40].

Figure 8. (a) Fragility and (b) apparent activation energy as a function of the VBTMAC weight fraction for the copolymers (squares) and their parent blocks (stars). Fragility data from dielectric measurements, taken from ref [29] are also included along with fragility data for PS taken from ref [40].

Noteworthy, the PVBTMAC homopolymer exhibits one of the lowest fragility values, ever reported for common polymers (see Figure S7 and Table S1), reflecting a superstrong behavior [41,42]. The rheology-derived values are in line with those found from dielectric measurements [29]. This low value of fragility indicates a less-cooperative character of the structural relaxation, meaning that less neighboring segments cooperate in the structural relaxation. Specifically, the PVBTMAC homopolymer exhibits distinctly reduced fragility values compared to the linear Polystyrene [40,43]. A similar trend has been observed in the family of poly(p-alkyl methacrylates), where a change from a “fragile” (m = 92) to a “strong” (m = 36) liquid occurs only by increasing the length of the side chain with the addition of a methylene unit (see Figure S8) [43,44]. Specifically, the PVBTMAC homopolymer exhibits a slightly lower value of fragility than poly(p-alkyl methacrylates) with side chain lengths, p, bearing 1 < p < 18 methylene units, [44,45,46] and the poly(p-phenylene) homopolymer,[47] bearing side chain length with 8 methylene units, despite the higher T_g of PVBTMAC. Therefore, the superstrong nature of the PVBTMAC homopolymer is probably driven by mainly its side chain length and its high T_g that is mainly dictated by the strong electrostatic interactions, taking place along its side chains.

Concerning the statistical copolymers, a similar superstrong behavior can be observed. Anticipately, as shown in Figure 8b, the apparent activation energy strongly increases by increasing the VBTMAC content, reflecting the stiff nature of VBTMAC segments and the higher amount of energy that is required for their segmental relaxation. To sum up, by analyzing the rheological results within the framework of the classical free volume theories of T_g, quantitative insight into the physical behavior of DHBCs can be obtained.

4. Conclusions

Herein, we investigate the mechanical properties of block and random DHBCs using rheological measurements. We report that the mechanical properties are governed mainly by the interfacial T_g. Depending on the VBTMAC content and block arrangement across the backbone, the macroscopic mechanical properties change from elastic-like to liquid-like. Specifically, the PVBTMAC homopolymer exhibits an elastic-response up to high temperatures, reflecting its strong nature. A viscoelastic response is evident for the statistical copolymer with 40 wt.% VBTMAC. By further decreasing the VBTMAC to 20 wt.%, the statistical copolymer exhibits a liquid-like response. Overall, the zero-shear viscosity, determined by fitting the measured data with two empirical models (i.e. Carreau-Yasuda and Modified Cross model), exponentially increases by increasing the VBTMAC content. Furthermore, for the 20 wt.% VBTMAC content, the change of block arrangement of the backbone from statistical to sequential results in a transition from liquid-like to elastic-like behavior, accompanied by an increase in zero-shear viscosity.

In terms of classical free volume theories [32], we report that the copolymers exhibit reduced fragility reminiscent with that found in the PVBTMAC parent block. Importantly, the PVBTMAC homopolymer exhibits 5-fold lower fragility than the one found for Polystyrene, reflecting its superstrong nature. The above observations are in line with previously reported dielectric results [29]. A superstrong behavior is also evident for the statistical copolymers, reflecting the impact of the glassy VBTMAC segments and their miscible state. To sum up, this study provides useful viscoelastic data related to densely brush copolymer that are promising for drug delivery applications.