Oleksii
Kotko
ab,
Petr
Šálek
*a,
Jana
Dvořáková
a,
Miroslava Dušková
Smrčková
a,
Ján
Šomvársky
c,
Jean Jacques
Bonvent
d,
Sérgio
Brochsztain
d,
Miroslav
Šlouf
a and
Vladimír
Proks
a
aInstitute of Macromolecular Chemistry, Czech Academy of Sciences, Heyrovského nám. 2, 162 00 Prague 6, Czech Republic. E-mail: salek@imc.cas.cz; Fax: +420 296 809 410; Tel: +420 296 809 225
bDepartment of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, 128 00 Prague 2, Czech Republic
cDepartment of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic
dUniversidade Federal do ABC, Av. dos Estados, 5001. Bairro Santa Terezinha, Santo Andre, SP, Brazil
First published on 25th June 2024
We report an innovative preparation of soft micron-sized polypeptide microgels by horseradish peroxidase (HRP)-mediated crosslinking in inverse suspension. The prepared microgels were based on poly[N5-((2-hydroxypropyl)-L-glutamine)-ran-(N5-propargyl-L-glutamine)-ran-(N5-(6-aminohexyl)-L-glutamine)]-ran-(N5-[2-((4-hydroxyphenyl)ethyl)-L-glutamine)] (P2HPG-Tyr) polymer precursor. We tested effects of three different surfactants, namely, sorbitan monooleate (SPAN 80), polyoxyethylenesorbitan trioleate (TWEEN 85), and dioctyl sulfosuccinate sodium salt (AOT), on microgelation in inverse suspension without or with a pre-emulsification step. The prepared P2HPG-Tyr microgels were investigated using light and cryogenic microscopy. The HRP-mediated crosslinking in inverse suspension employing SPAN 80 and one hour pre-emulsification yielded high-quality, spherical, and colloidally stable ∼80 μm P2HPG-Tyr microgels. Innovatively, we immobilized these large swollen P2HPG-Tyr microgels on mica and glass substrates for subsequent topography and surface nanomechanical measurements of these hydrated and swollen microgels using atomic force microscopy (AFM) in peak force quantitative nanomechanical mapping (PF-QNM) mode. The topography analyses revealed surface irregularities of the developed P2HPG-Tyr microgels consisting of small holes with diameters ranging from 80 to 200 nm. The PF-QNM proved the viscoelasticity and softness of P2HPG-Tyr microgels documented with Young's modulus in the range of tens of kPa derived from force-separation curves. Finally, the crosslink density was evaluated using two methods of calculation, revealing comparable concentrations of elastically active network chains (EANCs) in the range from 0.489 × 10−3 to 0.812 × 10−3 mol cm−3.
Fabrication conditions, composition, and physico-chemical properties of the final product predetermine the architecture and nature of microgels, which then define structure, mass density, softness, and mechanical properties. In other words, it refers to how the microgel internal structure and cross-linked network interact with the environment and macromolecular system and respond to external stimuli.16 Therefore, the mechanical properties, swelling, and softness of microgels are crucial parameters for potential applications in industry, biotechnology, and biomedicine. In particular, tailored soft microgels have become very attractive for bioapplications, such as tissue engineering, delivery systems, or cell encapsulation, because they meet the specific requirements for the mechanical properties of these soft hydrogel materials.17,18 Nevertheless, the research community has been facing a formidable challenge in quantifying the mechanical properties of soft or even ultra-soft hydrogel materials in a hydrated state, which has rarely been described in the literature in much detail.17,19,20 Particularly, this challenge is particularly profound for soft microgels because they operate in the nano- and microscale size ranges.18,21 According to the literature, a modulus of soft hydrogel materials is typically accepted in the range from ∼200 Pa to 100 kPa and that of ultra-soft hydrogel materials is in the range of ≤200 Pa.19,20
The mechanical properties of soft hydrated microgels can be characterized using a few established methods, including microfluidic-based approaches, micropipette aspiration, glass-capillary approach, and atomic force microscopy (AFM).20,22 AFM belongs to fundamental methods used to measure elasticity and nano- and micromechanical properties of soft microgels with Young's modulus (E), frequency-dependent loss (G′), and storage moduli (G′′).23 A significant advantage of AFM is the possibility of performing measurements under ambient conditions in a liquid environment, which is more suitable for the characterization of soft hydrogel materials. However, the accuracy of moduli measurements in a liquid environment may suffer from hydrodynamic forces between the AFM cantilever, probe and analyzed samples.24 In particular, AFM allows imaging of surface topography, as well as detection and capture of forces between the tip and the sample via peak force quantitative nanomechanical mapping (PF-QNM) mode. PF-QNM is an AFM imaging mode that tracks the surface of the sample while simultaneously acquiring the individual force curves for each intermittent individual tap of the surface of the sample using the AFM tip. The force curves can be later analyzed to obtain mechanical data, such as Young's modulus and/or reduced modulus. PF-QNM is advantageous for the analysis of hydrated soft materials, such as microgels, because it controls the forces between the AFM tip and the sample, thus reducing the deformation of the sample and the tip wear. However, this measurement is difficult to perform for the analysis of large swollen microgels in a liquid environment, where the stable fixation of the sample to the substrate and the immobility of the sample during measurement are very complicated. Moreover, there are very few publications that address this problem and propose effective solutions.
In this study, we aimed to prepare soft micron-sized polypeptide P2HPG-Tyr microgels using HRP-mediated crosslinking in inverse suspension. The effects of various microgelation conditions, including surfactant type and pre-emulsification step, were tested on P2HPG-Tyr microgel morphology, size, and particle size distribution, and the prepared microgels were studied using a light microscopy technique. We discovered that pre-emulsification is a crucial step in stabilizing the inverse suspension and obtaining spherical and colloidally stable ∼80 μm P2HPG-Tyr microgels. The next aim was to evaluate the nanomechanical properties of the developed P2HPG-Tyr microgels in the hydrated state. Therefore, they were successfully immobilized on mica and glass substrates. Then, topography and nanomechanical analyses of P2HPG-Tyr microgels swollen in Q-H2O or PBS buffer were performed by PF-QNM, providing topography images and Young's moduli derived from force-separation curves. The results demonstrated the surface irregularity, viscoelasticity and softness of the developed P2HPG-Tyr microgels.
The number-average molecular weight of the P2HPG-Tyr was Mn = 22100, the weight-average molecular weight was Mw = 29000, and the dispersity was Đ = 1.31 (Shimadzu HPLC-SEC system equipped with UV detector (Shimadzu, Japan), differential refractive index detector (Wyatt Optilab T-rEX), and multi-angle light scattering detector DAWN EOS (Wyatt Technology), Superose 6 column). The concentrations of tyramine and propargyl units were 0.69 (11 w%) and 0.14 mmol g−1 (2 w%), respectively. The content of the primary amine groups was around 0.02 mmol g−1 determined by the commonly used reaction with fluorescamine.
In the subsequent experiments, the microgelation procedure started with a pre-emulsification step for 1 h under stirring (1000 rpm), after which the stirring speed was reduced to 500 rpm and microgelation was initiated by the addition of H2O2 (6.4 μL).
(1) |
(2) |
(3) |
Bruker PF-QNM mode was employed to determine topography, Young's modulus (E) and reduced modulus (E*) of the reswollen microgel particles. Topography images of each sample were captured. The scan sizes were 5 × 5 μm, and the scan rate ranged from 0.1 Hz to 0.2 Hz. For each sample, 500 pairs of extend and retract force curves in trace and retrace directions were collected by real-time High Speed Data Capture interface on the center of the particles with a particle size of 80 μm (in Q-H2O) and 74 μm (in PBS buffer with pH 7.4). The force curves were analyzed using NanoScope Analysis 1.50 software. The E and E* values were collected from 500 pairs of retract force-separation curves for each sample. Then, the values were averaged, and their standard deviations (SD) were calculated.
To obtain the E values of the samples, the retract force-separation curves were fitted by the following equation according to the Hertz model:
(4) |
To obtain the E* values, the retract force-separation curves were fitted by applying the following equation using the Derjaguin–Muller–Toporov model:
(5) |
Microgels | Surfactant | Surfactant concentration (wt%) | Pre-emulsification | Dispersant for image analysis | D n (μm) | D w (μm) | Đ | Yield (%) |
---|---|---|---|---|---|---|---|---|
AOT – dioctyl sulfosuccinate sodium salt; Dn – number-average diameter; Dw – weight-average diameter; Đ – dispersity; SPAN 80 - sorbitan monooleate; TWEEN 85 – polyoxyethylensorbitan trioleate | ||||||||
M1 | SPAN 80 | 20 | No | Q-H2O | 47 | 128 | 2.7 | 67 |
M2 | SPAN 80 | 20 | 1000 rpm/1 h | Q-H2O | 80 | 127 | 1.6 | 57 |
M3 | TWEEN 85 | 15 | no | Q-H2O | 45 | 104 | 2.3 | 84 |
M4 | TWEEN 85 | 15 | 1000 rpm/1 h | Q-H2O | 25 | 36 | 1.4 | 90 |
M5 | AOT | 15 | no | Q-H2O | 33 | 59 | 1.8 | 64 |
M6 | AOT | 15 | 1000 rpm/1 h | Q-H2O | 11 | 17 | 1.6 | 50 |
First, we tested 20 wt% SPAN 80 as a steric stabilizer for the microgelation without the pre-emulsification step of P2HPG-Tyr. The final microgels (M1) were mainly coagulated and contained only a small number of 47 μm microgels (Fig. 1(a)). According to the literature, we decided to include the mechanical pre-emulsification step in the microgelation process to form a stable inverse suspension that can subsequently be microgelated by H2O2 addition.28Fig. 1(b) depicts that the mechanical pre-emulsification step significantly affected the microgelation of P2HPG-Tyr in the presence of 20 wt% SPAN 80. The individual and spherically shaped M2 microgels (swollen in Q-H2O) with Dn = 80 μm and Dw = 127 μm, and broad particle size distribution (Đ = 1.6) were formed.
The results indicated that the pre-emulsification step enabled the molecules of SPAN 80 to cover the droplets and, thus, effectively stabilize inverse suspension against undesired coalescence. Nevertheless, the microgelation yielded 57% of the product, indicating that not all the amounts of P2HPG-Tyr polymer precursor were incorporated into the final microgels due to the partial coalescence of droplets during microgelation. Besides, we suppose that the lower microgelation yield would be due to the hydrophobic character of SPAN 80 and its high concentration and higher viscosity, as already observed in our previous study on the preparation of polypeptide nanogels.26 Second, the microgelation was carried out in the presence of 15 wt% TWEEN 85 steric stabilizer (M3), resulting in aggregated 45 μm microgels (Fig. 1(c)). The pre-emulsification step helped to ensure the colloidal stability of the inverse suspension because individual spherical M4 microgels were fabricated with Dn = 25 μm, Dw = 36 μm, and Đ = 1.4 in the swollen state (Fig. 1(d)). The yield of microgelation was calculated as 90%, suggesting that TWEEN 85 effectively prevented undesired coalescence of droplets compared to stabilization using 20 wt% SPAN 80 (M4). However, during this microgelation, we encountered one major problem: the reproducibility of the preparation of microgels in the presence of TWEEN 85. We suppose that TWEEN 85 might have negatively affected the enzymatic activity of HRP; therefore, the microgels could not be reproducibly prepared. Third, 15 wt% AOT was used as a steric stabilizer for microgelation. The stabilization of inverse suspension was slightly improved by AOT because more individual P2HPG-Tyr microgels (M5) were obtained (Fig. 1(e)). Besides a few irregular objects, M5 contained spherical microgels (swollen in Q-H2O) with Dn = 33 μm, Dw = 59 μm, and Đ = 1.8. Surprisingly, the pre-emulsification step had a deteriorating effect on the microgelation of P2HPG-Tyr in the presence of 15 wt% AOT (M6). Fig. 1(f) depicts mainly aggregated products with few number of 11 μm microgels. The microgelation in the presence of the AOT surfactant also resulted in low yields, which was probably due to electrostatic repulsion between the AOT surfactant and P2HPG-Tyr polymer precursor.26
Our results clearly demonstrated that the pre-emulsification step contributed to the formation of a more colloidally stable inverse suspension, which was then more effectively microgelated, and individual P2HPG-Tyr microgels were fabricated in the presence of SPAN 80 as a steric stabilizer (M2). We also evaluated morphology, particle size and particle size distribution of M2 swollen in PBS buffer with pH 7.4. As observed in aqueous M2 suspension, M2 microgels swollen in PBS buffer maintained their spherical shape and smooth surface. The change in pH to 7.4 also led to narrowing of the particle size distribution (Đ = 1.4) and a decrease in M2 diameter to Dn = 74 μm and Dw = 103 μm (Fig. 2) due to stronger hydrophobic interactions and hydrogen bonding between P2HPG-Tyr chains in M2.29
Scheme 2 Immobilization of swollen P2HPG-Tyr microgels on APTES-modified mica and glass substrates (created with BioRender.com). |
Fig. 3(a)–(d) shows AFM images of swollen M2 under various conditions. Interestingly, PF-QNM topography analyses revealed that M2 surface irregularities in both environments were not visible during light microscopy analyses due to a lack of necessary magnification. These observations were attributed to dimples in swollen M2. In general, AFM does not belong to the standard techniques for the characterization of porous structures. However, it can provide relevant information about surface properties of hydrated and swollen hydrogel samples under optimized, reliable, and stable conditions as it was, for example, demonstrated with carboxymethyl guar gum and agarose hydrogels.33,34 M2 is composed of covalently crosslinked P2HPG-Tyr polymer chains via dityramine crosslinks into 3D P2HPG-Tyr network.25 When M2 was swollen, it was permeated with a solvent enabling a conformational change from collapsed to extended state.17 According to PF-QNM analyses, M2 showed surface irregularities consisting of small holes with depths ranging from 80 to 200 nm in diameter. A similar observation of irregular surface structure was found with swollen poly(2-hydroxyethyl methacrylate) hydrogels with various crosslinking densities.35 Moreover, our assumption can be supported by the fact that Fig. 3(a)–(d) illustrates that the PF-QNM analyses were performed on the spherical surface of a single M2 microgel because the color change from dark to bright can be observed in the images, as illustrated in Fig. 3(b)–(d). In other words, the surface irregularities were visible only in the central region of the PF-QNM images. Therefore, we can rule out the possibility that light areas represent small microgels surrounding the studied ∼80 μm M4 microgel (in Q-H2O) or ∼74 μm M2 microgel (in PBS buffer) because they are observed as light-colored objects in dark areas. Nevertheless, the size of the irregularities is too small in comparison to the diameter of M2, and it is still possible to consider the investigated surfaces of M2 as smooth.
Fig. 3 PF-QNM topography height images of P2HPG-Tyr microgels on mica substrate (a), (b) and glass substrate (c), (d), swollen in Q-H2O (a), (c), and PBS buffer (b), (d). |
Fig. 4 Cryo-SEM micrographs showing the morphology of frozen M2 microgels at (a) lower magnification and (b) higher magnification. |
Fig. 5(a)–(d) shows the force–separation curves of swollen M2 microgels immobilized on two different substrates, mica and glass, in Q-H2O and PBS buffer at pH 7.4. On the extended curve in Fig. 5(a), there is an attractive interaction at ∼180 nm between the swollen M2 in Q-H2O and the tip. The interaction between the tip and the swollen M2 then becomes slightly repulsive and is followed by the strong attraction of the tip to the sample. After the tip touches the surface, the attractive forces increase to approximately 1.8 nN. On the retract curve, the interactive forces decrease gradually, while the obvious hysteresis and slight adhesion are attributed to viscoelastic relaxation and squeezing out of Q-H2O from swollen M2.37
Fig. 5 Force–separation curves of swollen M4 on mica (a), (b) and glass (c), (d) substrates in Q-H2O (a), (c) and PBS buffer with pH 7.4 (b), (d). |
On the extended curve depicted in Fig. 5(b), there is weak repulsion from 200 nm to 190 nm, followed by gradual weak attraction, depicted from 190 nm to 0 nm. During retraction, the swollen M2 adheres and is stretched by the retracting tip with almost no attractive or repulsive interaction afterwards.
Fig. 5(c) demonstrates strong and gradual attraction until ∼20 nm of the extended curve and rapid drop due to the repulsion of the tip from the surface, while the retract curve illustrates the continuous decrease in tip-sample interaction until there is no repulsion or attraction. During the nanomechanical measurement of swollen M2 in Q-H2O, we also observed hysteresis due to the viscoelastic behavior and drainage of Q-H2O.37
As depicted in Fig. 5(d), the tip-to-sample approach occurs with weak repulsion, which is then followed by the gradual weak attraction mostly visible in the 125-nm to 0-nm part of the separation axis; the retract curve shows a continuous decrease with no repulsion or attraction.
As our observations revealed, the nanomechanical properties of swollen M2 were sensitive to aqueous environments with different pH and salinity levels. PF-QNM analyses of swollen M4 in Q-H2O on mica and glass substrates demonstrated softer behaviors documented with E values (Table 2). It was also obvious that swollen M2 was more load-dependent during analyses in Q-H2O in comparison with PF-QNM analyses in PBS buffer with pH 7.4. The force–separation curves demonstrated that PBS-swollen M2 was not so responsive to contact with the tip and had stiffer behavior documented with increased E values on the glass substrate in PBS (Table 2). Simultaneously, the PBS-swollen M2 on mica demonstrated slightly lower E values than the Q-H2O-swollen M2 on mica (Table 2). However, the lower tip-sample interactions, which were observed during PF-QNM analysis of PBS-swollen M2 on mica (Fig. 5(b)), suggest that lower tip-sample interaction yields lower E values. This analysis also confirmed the viscoelasticity of swollen M2 because the E* values shifted to higher values compared to the E values (Table 2).
Substrate | Environment | Young's modulus (E ± SD) [kPa] | Reduced Young's modulus (E* ± SD) [kPa] |
---|---|---|---|
Mica | Q-H2O | 40.2 ± 16.2 | 53.6 ± 21.6 |
Glass | Q-H2O | 50.9 ± 14.9 | 67.8 ± 19.8 |
Mica | PBS buffer | 35.7 ± 15.1 | 47.6 ± 20.1 |
Glass | PBS buffer | 60.9 ± 13.4 | 81.2 ± 17.8 |
In summary, the calculated Young's moduli were in the range of tens of kPa, indicating soft hydrogel materials. For example, Dvořáková et al. prepared the injectable hydrogels from a P2HPG-Tyr polymer precursor modified with integrin-binding arginine–glycine–aspartic acid peptide by varying the concentrations of the P2HPG-Tyr precursors and horseradish peroxidase as well as the nH2O2/nTyr ratio. The mechanical properties of the injectable hydrogels were characterized by oscillatory rheology measurements with storage moduli ranging from 1 to 4 kPa, indicating ultra-soft hydrogel materials.15 In general, there is clear and practical evidence that the softness of hydrogel materials is influenced by crosslink density.
Fig. 6 A – hydrogel network structure formed by crosslinking of primary polyfunctional P2HPG-Tyr chains via linking of tyramine units, i.e. the depicted network is crosslinked with the dityramine crosslinks. Example A is given for the situation depicted in Fig. 7(A), i.e. the dityramine bonds issue maximally 4 bonds to the hydrogel 3D network structure, and the internal dityramine chains are not considered elastically active; insert B shows the two possible chemical structures of dityramine links; and panel C shows a single tyramine unit in its all possible bonding states as treated by the theory of branching processes found in the crosslinking system: in the starting backbone chains, the units P0 with three unreacted bonds do not exist, while the units P1 with only one connection to backbone chains are possible (outermost units) and the units P2 represent the most probable state of tyramines in initial system, i.e. the T-units are incorporated in the primary P2HPG-Tyr chains. Unit E3 demonstrates that the trifunctional fully reacted tyramine unit embedded in the hydrogel network, an elastically active crosslink depicted in Fig. 7(B). |
The tyramines are crosslinking the P2HPG-Tyr primary chains by their mutual coupling. The formed dityramine bonds can attain two possible chemical types, as depicted in the insert in Scheme 1 and Fig. 6. The two possible types of dityramine links are similar in size. However, the biphenyl-containing units presumably possess higher rigidity. It has already been reported in the literature that the major part of dityramine bonds attains the biphenyl structure, i.e. the more rigid bonds prevail.39
Thus, for the calculation of the concentration of EANCs, we consider both situations delimiting the possible real behavior of gels: i/the dityramine links between the backbone chains are considered single four-functional crosslinks of a rigid nature, and their internal segment does not contribute to the number of elastically active chains (Fig. 7(A)), or, ii/the connecting dityramine link is considered sufficiently flexible and contributing to elasticity of the network; then, each tyramine unit provides a three-functional crosslink (Fig. 7(B)).
Later, we also briefly address the rather general issue of the minimal chain length between the elastically active crosslinks to exert the rubbery elasticity.
In the scheme in Fig. 6, the general structure of the hydrogel network is shown and the basic structural features of the network are illustrated. The primary P2HPG-Tyr chains are combined through 4-functional, 3-functional, and bifunctional dityramine links, and some chains can be attached as monofunctional parts through a monofunctional “T-link”. (The adjective “functional” describes the number of connections of the given unit with the infinite network, as illustrated in Fig. 6(C)). In the “monofunctional case” (not shown in Fig. 6(A)), indeed, the attached part of the material forms a dangling chain and does not contribute to the elastic response.
First, the crosslink densities of hydrogels in both limiting states were inferred from the system's starting composition and from the parameters determined during the characterization of the P2HPG-Tyr polymer precursor (such as the molecular weight of the precursor – Mn = 22100 g mol−1, the content of the crosslinking units (tyramines) – 10.8 wt%; thus, the average number of crosslinkable units per chain is 12).
Let us distinguish units in which all chains are composed by the number of issuing bonds to an infinite network (arrows in Fig. 6), i = 0, 1, 2,…, (cf. unit states in Fig. 6(C)) with molar concentrations ci and molar fractions ni = ci/c, where and Mi is molar mass. Crosslinks are units with at least 3 issuing bonds to an infinite network, i ≥ 3. In our case, i = 3 belongs to reacted tyramine units (see unit E3 in Fig. 6(C)) or 4 belongs to dityramine bonds. Each bond issued from a crosslink represents 1/2 of an elastically active network chain. Therefore, the number (of moles) of EANCs (per unit volume), i.e., the molar concentration of EANCs is . However, molar concentrations ci are not known or measurable directly, whereas the molar fractions, ni, are. Molar concentration c can be obtained from the specific gravity, , where m and V are the mass and volume of the whole system, respectively, and νe can be expressed in terms of hydrogel composition ni as follows:
(6) |
To calculate the crosslink density for situation A in Fig. 7, let us assume that the average number of 3-functional T-links (such as the units P2 or less likely P1 in Fig. 6(C)) is 12 per a primary chain of 22100 g mol−1. Because the two 3-functional crosslinks are consumed for one 4-functional dityramine bond, the number obtained by the application of eqn (6) is further divided by a factor of two; thus, the value of νe,4 is 0.542 × 10−3 mol of EANCs per 1 cm3 of the dry network.
In situation B of Fig. 7, the number of 3-functional crosslinks is equal to the number of fully reacted tyramines connected to the infinite network, such as units E3 in Fig. 6(C). Then, corresponding to the conversion of tyramine coupling reactions close to 1, the final νe,3 is 0.812 × 10−3 mol cm−3. Subsequently, the difference between the limiting network structures with either crosslink type Δν is 33% (related to the value higher of the two values, νe,3).
A more refined way leading to a value of νe corrected for all possible bonding states of crosslinking units was based on the schooled application of the statistical theory of branching processes (TBP).40 The application of TBP on multifunctional crosslinking chains is explained in detail in the work.41 Briefly, applying the TBP, one examines all the possible connections between units existing at a given state of the crosslinking process. The units are distinguished according to their number of bonds in all reaction states: unreacted bonds, bonds reacted but issued to a finite structure, and bonds reacted and issued to an infinite network structure. See Fig. 6(C) for an example of a single tyramine unit. The TBP algorithms provide the average concentrations of given units in the system, while the inactive structures that are statistically present in every real network are not counted. In other words, the calculation considers the loss of units in the dangling chains (example in Fig. 6(A): primary chain F and other chain ends) and in the possible sol part.
A mathematical tool enabling this analysis is the probability generating function (PGF) derived in this case for the given case of multifunctional chains. The PGF provided the result through a solution of a system of differential equations. A detailed discussion of these derivations exceeds the scope of this paper but will be made available to the reader on request. We used a script written in the software Wolfram Mathematica 14: the solution of the simulation of the network state at a complete conversion (α = 1) gave the values of νe,3 = 0.677 × 10−3 mol cm−3 and νe,4 = 0.489 × 10−3 (see Table 3 for a summary). The estimate from the system composition is very reasonable. Moreover, the simple estimate gives higher values because it does not count off the elastically inactive bonds, unlike TBP. Particularly, the units situated in the dangling chains or appearing in the chain ends negatively contribute to the value of νe. Thus, the TBP shows, by a statistical treatment of the given system, that approximately 10 (for fe = 4) and 17% (for fe = 3) of bonds belonging to crosslinkers are connected with elastically inactive material. The set of results in Table 3 provides good evidence of the relevancy of the estimates. It is also worth mentioning that (1) the value of νe determined for the hydrogels corresponds to the crosslink density of moderately crosslinked synthetic hydrogels based on poly(2-hydroxyl methylmethacrylate)42 or falls within a range of crosslink densities of chemically similar hydrogels based on a copolymer of four types of (meth)acrylamide units crosslinked with aromatic azo bonds designed previously for drug delivery application.43
Method of calculation | Crosslink density νe [mol cm−3] | |||
---|---|---|---|---|
Parameters | ν e,4 f e = 4 | ν e,3 f e = 3 | (νe,3 − νe,4)/νe,3 | |
Composition of hydrogel eqn (6) | Chain length, g mol−1 number of tyramine units per chain maximal functionality of crosslink | 0.542 × 10−3 | 0.812 × 10−3 | 0.333 |
Theory of branching processes | 0.489 × 10−3 | 0.677 × 10−3 | 0.277 |
Interaction parameter χ | ||||
---|---|---|---|---|
Parameters | ν e,4 f e = 4 | ν e,3 f e = 3 | χ ν e,4 = χνe,3 | |
Swelling of hydrogel eqn (8) | φ 2 | 0.094 | 0.404 | |
φ 0 | 0.04 → 0.094 | |||
front factors A, B | A = 1, B = 2/4 | A = 1, B = 2/3 | ||
V s, cm3 mol−1 | 54 | |||
v e – TBP | 0.489 × 10−3 | 0.677 × 10−3 |
A legitimate question arises if all the segments constituting the hydrogel network are long enough to return the elastic work. In other words, are the chain segments between the branched sides exerting entropic elasticity? The distribution of crosslinkable units along the backbone of the random copolymer is indeed statistical. This means that some tyramine units can be placed tightly next to each other or separated by 1,2,3…Nmax units. The average length of chains between the two tyramine units in the P2HPG-Tyr backbone is 8 units. Let us analyse the behaviour of the N-jointed polymer segments within the basic polymer physics paradigm of the freely jointed model44 and calculate the distribution of the distances between the chain ends from the minimal number of two segments. The result is quite remarkable, and the end-to-end distance (ETED) of already 3 jointed segments revealed maxima on the ETED distribution curve (Fig. S2 in ESI†). This means that if such a chain is strained using force and its ends are displaced outside of the maximum intensity of ETED counts, the ends tend to “come back” to their most probable distance once the displacement is no longer maintained by force. Therefore, it follows that 3 segments already possess entropic elasticity. Moreover, the distribution function does not dramatically differ with the number of segments (Fig. S2 in ESI†). Indeed, the length of a “typical” segment in a real system, which could perhaps substitute one bond in a freely jointed model, is the subject of a complex assessment. It is quite clear that due to the limited rotation and various stiff structures, such characteristic segments must be longer than a single covalent bond. In our copolymer, each incorporated unit is contributed by two or three covalent σ-bonds into the P2HPG-Tyr backbone. Let us consider the backbone sequence of a monomer unit to be a stiff segment. The reasoning above and the results of the calculation of ETED show that all connections between tyramine units from the N ≥ 3 can be considered elastically active. The molar fraction of these connections is more than 98 molar% of all connections between tyramine branch points; see Table SI in ESI.† Thus, the resulting values of crosslink densities can be taken as very close approximations, and a correction for the fraction of elastically inactive chains was not adopted.
Finally, we considered calculating hydrogel network parameters based on their physical behavior, specifically on their equilibrium swelling tackled experimentally. We characterized the swelling of microgel particles from their dry and swollen diameters obtained from the light scattering experiment, resulting in a volume fraction of swelling φ2 = 0.094. The equilibrium swelling volume fraction is defined as follows:
(7a) |
(7b) |
The balance between the number of solvent molecules penetrating the network chains, process driven osmotically, and the network elastic retraction force driven by the entropy of the network chains determines the equilibrium swelling for a given solvent and temperature. The retraction force is proportional to the concentration of EANCs. Therefore, we should be able to calculate the concentration of the retracting chains, νe, using the well-known swelling equation, the Flory–Huggins–Rehner model, in the following form:45
(8a) |
(8b) |
The outcome of the relation above was very interesting: when the value of φ0 was 0.04 (in consent with real preparatory conditions). For the case of trifunctional crosslinks and experimental φ2 of 0.094, swelling eqn (8,a) surprisingly provided a negative value of crosslink density for a range of χ. Because the Flory–Huggins–Rehner model is derived from thermodynamic principles and the well-established rubbery elasticity theory, we attribute this limiting behaviour of eqn (8) to an existing physical effect, unknown at the current time. Tentatively, it seems that the formation of a network at φ0 = 0.04 would not be physically possible for the given composition. In fact, when the network is formed in such a highly diluted system, the precursors separated in space must come together to make crosslinks, while the solvent volume exceeds the maximum network capacity obtained from φ2. When the first network is formed, the excess solvent is excluded from the crosslinking system. Thus, in eqn (8b), we use the value 0.094 for φ0 to approximate our experimental circumstances. Interestingly, the obtained χ did not depend on functionality, i.e. on parameter B, and was 0.404 for both considered structures. This value of the constant interaction parameter falls within a sound range for aqueous hydrogel and will serve as a starting point in future investigations of the swelling behaviour of the novel P2HPG-Tyr-based networks.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ma00356j |
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