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Chapter 1
Polymer Gels: Basics, Challenges, and Perspectives Ferenc Horkay*,1 and Jack F. Douglas 1Section
on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, United States 2Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States *E-mail:
[email protected]. E-mail:
[email protected].
Recently, there has been a sharp increase in the number of theoretical and experimental studies made on gels to address various aspects of chemistry, physics, and applications of these structurally complex ‘soft’ materials. In this introductory chapter, we briefly discuss the classification of gels with an emphasis on the unique structural features and properties of this class of materials. Recent advances in emerging areas are also addressed, along with challenging unsolved problems, and possible future research directions are identified. Our personal perspective on this vast scientific field is mainly intended to convey the many potential opportunities for advancing our understanding of gels through advanced experimental, and theoretical investigations to enable the design of novel gel materials with rationally engineered physical, chemical and biological properties.
© 2018 American Chemical Society Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
Introduction Gels are a common form of soft matter that arises from diverse associating small molecules, polymeric, and particle components. However, the utilization of gels in numerous industrial and medical applications requires a better understanding of the process of gel formation, factors that influence gel stability, and relations between the structure and the unique rheological properties of this class of materials. Gelation encompasses diverse processes in which molecules or particles mutually interact with each other and the solvent in such a way as to become localized in space, leading to the emergence of macroscopic rigidity. Amorphous solidification process can occur either as an equilibrium thermodynamic transition or a non-equilibrium dynamical transition, and as thermally reversible or irreversible processes. Although many gels involve chemical cross-links, as in the case of rubbery materials, the constraints that lead to molecular and particle localization can also imply dynamic associations and topological interactions between extended anisotropic molecules and particles. Polymeric gels created through the introduction of cross-links between polymers in solution are perhaps the most familiar type of gel material in manufacturing applications. Cross-linked gels are often relatively robust when subjected to large deformations, and capable of absorbing a large amount of solvent when the polymer and solvent have a high affinity. The properties of cross-linked gels can be tailored by controlling the polymer chemistry and the chemical synthesis conditions. The mechanical strength of these materials is often augmented by incorporating filler particles and other additives that can form their own network with the polymer gel matrix. Although gel behavior has been studied for many decades, the rational engineering of the properties of these complex materials requires a better understanding of the relationship between the molecular structure and the physical properties. This chapter briefly reviews the classification of gels with an emphasis on ‘classical’ cross-linked polymer gels, although we also discuss various types of physical gels where association or topological interactions are responsible for the gelation or amorphous solidification. We also mention some recent advances in the field of gels, along with unsolved problems and suggest possible future research directions.
Classification of Gels As mentioned before, the bonding in gels can be either physical or chemical in nature (1, 2). Physical cross-links include hydrogen bonding, hydrophobic interaction, inter-chain entanglement interactions of topological nature, and local crystallite formation. Although physical cross-links are not permanent, they are sufficiently strong to link together chain segments over a long timescale to influence the mechanical response of the network to an imposed perturbation. The lifetime of physical bonds normally depends on the temperature and other thermodynamic variables, making these systems thermally reversible and self-healing. 2 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
In Table 1 the major classes of gels are listed.
Table 1. Typical gels Type of cross-link Chemical gels
Procedure
Example
Cross-linkig of existing polymer chains in random (vulcanization) or end-linking process
rubber poly(vinyl alchol) gel
Cross-linking polymerization
poly(acryl amide) gel
Addition polymerization
silicone gel (addition cure)
Condensation polymerization Physical gels
silicone gel (condensation cure)
Formed by physical (e.g.. hydrogen) bonds
‘jello’ agarose gel
Formed by crystallization
cellulose gel
Formed by ionic bonds
gelatin gel
Formed by self-assembly of small molecules (e.g., organogelators)
steroid gel
Formed by mechanical dispersion of carbon nanotubes in polypropylene
carbon nanotube entanglement network
Chemically Cross-Linked Gels Chemically cross-linked gels are formed by covalent cross-linking of polymer chains. Chemical gels are typically made by free radical polymerization, electromagnetic radiation (light, gamma, x-ray, electron beam), and by addition or condensation polymerization. Cross-linking by both free radical polymerization and electromagnetic irradiation involves three major steps: initiation, propagation, and termination. After initiation, the free radical site propagates and forms a network beyond the critical gelation point. Electromagnetic radiation can produce gels without the addition of a cross-linker. A further advantage of the latter cross-linking method is that it can be used at room temperature and at physiological pH. In addition and condensation polymerization processes, a multifunctional cross-linking agent reacts with the monomer units initiating chain growth. Anionic and cationic polymerization can also be used to make gels; however, these methods are sensitive to water, and therefore, their application is limited to non-polar monomers, i.e., cannot be used to synthetize hydrogels. The formation of covalent cross-links alters the chemical structure of the polymer, which has significant consequences on the physical properties of the system on both molecular and supramolecular levels. The type and degree of cross-linking influence many network properties, such as swelling, elastic, and transport properties. Cross-linking makes the polymer insoluble, independent of 3 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
the thermodynamic quality of the solvent. However, polymer networks are able to absorb solvent molecules. The driving force of the swelling process is the osmotic mixing pressure of the polymer Πmix. In a particular solvent, the degree of swelling is governed by the cross-link density of the polymer. Uncross-linked polymers can be diluted infinitely. Cross-links prevent infinite swelling because IImix is counter-balanced by the elastic pressure IIel generated by the cross-links. At equilibrium the solvent transport stops, and the swollen network coexists with the solvent. In other words, the swelling pressure IIsw becomes zero (3–5),
Equation (1) is based on the concept of additivity of the elastic and mixing free energies (4), and this assumption is widely used to analyze the swelling behavior of cross-linked polymer gels. The validity of this separability approximation is an important question, along with the nature of IIel when the polymer concentration is high so that mutual interparticle interaction effects are large (6). ‘Weak’ and ‘Strong’ Gels Many materials exhibit a highly compliant ‘jelly-like’ consistency rather than a fully solid like ‘gel’ character. This ‘squishy’ rheological response, so useful in so many applications and found in diverse common materials, is evidently intermediate between the ideal Newtonian fluid and Hookean elastic solid. In viscoelastic fluids, the elastic response is observed as a transient phenomenon, as first modeled by Maxwell, and the material flows after long times- ‘long’ often being a matter of human patience. Even crystalline solids will ‘flow’ given enough time so that stress relaxation with time t in viscoelastic materials does not in itself ensure the existence of a finite fluid viscosity η. This phenomenon is not exceptional, but is rather typical in everyday materials. Such materials may be termed ‘weak gels’ since they have an infinite viscosity, while at the same time they have a vanishing equilibrium shear elastic modulus. An infinite viscosity only requires the stress to decay sufficiently slowly. Given the ubiquity of this intermediate form of matter, some technical discussion is helpful to appreciate its nature and origin. The standard rheological characterization of gel materials is normally performed in the frequency domain by subjecting the material to a small oscillatory deformation and measuring the stress response to this perturbation. The most commonly measured properties are the ‘elastic modulus’ or ‘storage modulus’ G′ and the ‘viscous modulus’ or ‘loss modulus’ G″ obtained from the Fourier transform of the shear relaxation function, G(t). A ‘fully developed gel’ or ‘strong gel’ has the property G′ > G″, where both moduli (especially G′) are nearly independent of frequency ω over a large ω range. As noted before, such an elastic response to shear deformation ultimately derives from the presence of localized particles or molecules that store the deformation energy over long timescales. The existence of a linear stress-strain relation (Hooke’s law) implies that the material has a finite equilibrium modulus G. 4 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
The transition between a viscous fluid to a solid gel with a non-zero shear modulus Go is a progressive rheological transition and many equilibrium materials that we classify as being ‘gel-like’ exist in a state in which both G’ and G” are strongly frequency dependent. We term this type of intermediate material state a ‘weak gel’. These materials exhibit univeral properties associated with the emergence of the solid state that are rather distinct from ordinary Newtonian liquids and Hookean solids. The differece between the rheological behavior of weak and strong gels is illustrated schemitacally in Figure 1.
Figure 1. Schematic representation of the frequency dependence of the elastic modulus G’ and viscous modulus G” for strong and weak gels. It has been shown (7) that stress relaxation in systems undergoing amorphous solidification exhibits a universal power-law form, reflecting emergence of power correlations in the strain field of the gel material that often reflects the underlying hierarchical structure of the system. Specifically, the onset condition for forming a gel requires that the stress relaxtion function takes a power-law form,
so that the Fourier-transformed counterparts, G’ and G”, are likewise power laws in frequency, ω. In Eq. (2) S is a material constant and t is the time. Winter and coworkers (8, 9) have appropriately emphasized the emergence of power law scaling in G(t) as the defining condition for the emergence of the gel state. The shear viscosity is obtained from the integral of G(t) over finite times and this 5 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
quantity is divergent when G(t) takes the form of Eq. (2) so that η of a ‘weak gel’ is infinite. An infinite viscosity is a necessary condition for the solid state and this property provides a rationale for calling such materials “gels”. On the other hand, the power-law form of G(t) means that an applied stress will eventually decay to 0 at long times so that these materials ultimately relax as liquids. Thus ‘weak gels’ are a form of matter that is ‘intermediate’ between Newtonian liquids and Hookean solids (10–13). The exponent μ quantifies the precise degree of rheological ‘intermediacy (14, 15)’ and appears to vary with the type of the gel forming material. The determination of μ is presently phenomenological and research should be directed towards its better molecular understanding. While weak gels are arguably only a transitionary condition on the way to ‘proper’ gel state in which the material acquires a non-zero equibrium shear modulus G, this physical state is a prototypical condition for numerous everyday forms of ‘soft matter’ in living systems and soft materials encountered in manufacturing applications. From a practical standpoint, to estimate η and G raises issues since neither of these quantities are strictly speaking defined for weak gels. In practice, the frequency dependent extensions of η and G depend strongly on the measurement frequency so that a wide range of η and G values may be reported for gels if they are inappropriatly treated as Hookean solids or Newtonian liquids. Instead of η and G, these materials are characterized by the prefactor in Eq. (2), denoted by S by Winter and coworkers (8, 9), which has units involving fractional powers of time which characterize both the capacity of the material to store and dissipate energy. More theoretical and experimental work is needed to understand this important material property which is presently treated as purely a phenomenological parameter. The high degree of ‘softness’ of weak gels makes them susceptable to material change by perturbation. Some of their most characteristic and useful properties derive from this sensitivity and their self-healing when the perturbations are removed and the equilibrium state is recovered. In the next section, we discuss the nature of this highly non-linear response to describe property changes in these ‘susceptable’ materials. Responsive Gels A hydrogel is considered stimuli responsive, when minute changes in the environmental conditions (e.g., pH, ionic strength, temperature, solvent composition) induce a dramatic change in its properties (e.g., swelling degree, elastic modulus). In biomedical applications, stimuli responsive hydrogels are frequently called smart or intelligent gels, because response to different stimuli is a common feature of living systems. In smart gels, the structural changes must be fast and reversible, which make these systems of great interest in medical/biomedical applications (16, 17). Early studies on stimuli-responsive gels focused on the construction of artificial muscle-like materials. More recent studies aim to develop sensors, drug delivery, systems, scaffolds for tissue engineering, etc. Many applications require not only short response time (e.g., swelling-shrinking) but also the capability of the system to undergo large number of cycles without significant structural 6 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
destruction. Only relatively limited number of stimuli-responsive gel systems are available that exhibit optimized properties. Stimuli sensitive gels are based on the principle that polymer chains undergo conformational changes resulting in gel volume changes. This process reflects the change in the interactions between the components within the gel. For example, in pH and ion responsive gels volume transition is induced by changing the ionization of the polyelectrolyte chains. Decreasing the degree of ionization, the electrostatic interaction between the charged groups on the polymer chains is gradually reduced, and ultimately leads to the collapse of the network. In temperature sensitive systems the strength of polymer-solvent contacts varies relative to the polymer-polymer contacts. In a polymer solution, the polymer separates into a concentrated and a diluted phase at the critical temperature. When the polymer is cross-linked the gel undergoes a volume transition. Poly-N-isopropylacrylamide (PNIPAAM) is the most extensively studied temperature sensitive gel system. As the temperature increases PNIPAAM chains undergo conformational changes and the gels shrink at 40 °C. The swelling-shrinking process is reversible in these materials. Responsive gels are widely used as drug delivery devices to carry drugs to a specific site in the body. There is also strong interest in the application of responsive gels as biosensors in the medical field. A broad range of biomolecules of medical significance has been investigated. For example, glucose sensors are successfully used in insulin delivery systems (18). Work in this area is intense; trying to overcome challenges such as poor stability, hysteresis and long response time. In biomedical applications, a further critical requirement is to make the hydrogels biocompatible. An important emerging application of smart gels is tissue engineering (19). Smart hydrogels are well suited materials for scaffolds because (i) they provide the required aqueous environment for the cells, and (ii) they can release the cells in response to a stimulus. For example, it has been reported that PNIPAAm gels are capable to bind chondrocytes (cartilage cells) above the critical temperature and release them below the critical temperature (20). In tissue engineering application biodegradability of the gel scaffold and lack of cytotoxicity are also important requirements. Natural and Synthetic Polyelectrolyte Gels Biomacromolecules are naturally occurring polymers which are essential components of all living systems (21, 22). There are three major types of biopolymers: polysaccharides, proteins, and polynucleotides. Cellulose is the most abundant polymer in living systems. Many biopolymers, such as polypeptides, polynucleic acids, and certain polysaccharides are polyelectrolytes, i.e., charged macromolecules. In general, biological tissues are highly swollen polyelectrolyte gels. For example, the major component of cartilage extracellular matrix (ECM) is the negatively charged aggrecan/hyaluronic acid complex. The microgel-like aggrecan/hyaluronic acid assemblies provide the osmotic resistance of cartilage to external load (23). In other biological systems, e.g., in the nervous system, 7 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
Na+, K+, and Ca2+ ions regulate the excitability of neurons (21). Intracellular Ca2+ ions play important role in a variety of physiological processes such as muscle contraction, hormone secretion, synaptic transmission, gene expression, etc. Synthetic polyelectrolyte gels have a variety of applications in materials science and engineering, including materials for energy storage, separation, and drug delivery (24). The precise control of the molecular and supramolecular architecture of polymer gels makes it possible to design novel polyelectrolytebased materials in which the constituents are organized across multiple length scales to address a wide range of technological challenges. Since water is the medium of living systems, most biophysical gels are also polyelectrolyte gels, this class of gels heavily overlaps with those described in the previous sections. Polyelectrolyte gels have a great potential not only for designing new functional biomaterials (e.g., artificial muscle) but also understanding the principles of complex biological systems. Progress in the field requires an interdisciplinary effort to accomplish a better understanding of the structure and interactions of polyelectrolyte gels over multiple length and time scales. Gels Formed by Self-Assembly from Low Molecular Mass ‘Gelator’ Molecules Gels made from low molecular mass organic gelators (LMOGs) represent a relatively new class of soft materials (25, 26). In these gels, the monomer units self-assemble into fibrillar networks that entrap solvent molecules. The aggregation of gelator molecules is driven by a combination of directional non-covalent interactions (e.g., hydrogen bonding, π-π stacking, dipolar, quadrupolar) and non-specific and isotropic van der Waals interactions, rather than chemical cross-links (27). Often the directional interactions lead gelator molecules to self-assemble into chain-like structures glued together laterally by van der Waals interactions, resulting in the formation of highly extended fiber structures. The bundles, in turn, often form higher order secondary structures such as fibers, ribbons, sheets, etc. Although these gels commonly exhibit branching associated with defect formation in the fiber growth process, gelation can also arise from the extremely slow relaxation of disorganized suspensions of long uncrossable fibers, illustrating the phenomenon of gel formation without any cross-links (28). An outstanding question is what controls the diameter of these fibers. which is typically on the order of 10 nm (29). The physical factors governing the fiber branching is another basic feature that is not well understood and which greatly influences the mechanical properties of the resulting gel. Typically, gels from LMOGs are made by warming the material in a carefully selected solvent until the solid component completely dissolves and then cooling the resulting solution below the gelation temperature. During the cooling process, the gelator molecules start to phase separate. Three different scenarios may occur: (i) an ordered phase develops (e.g., crystals are formed), (ii) an amorphous phase develops due to random aggregation of the primary molecules, and (iii) a gel is formed. Gel formation depends on the interactions between the gelator and solvent molecules. It is known that a stable gel requires high melting temperature of the 8 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
gelator and low solubility in the liquid at room temperature. Gelators with higher solubilities are less suitable for network formation, and therefore they should be applied at higher concentrations. Furthermore, both gelator structure and solubility modulate the self-assembly process. A significant research effort has been devoted to identifying potential gelators by screening a variety of molecules using an Edisonian or ‘combinatoric’ approach, as well as by testing solvents that may be suitable to form gels using solubility parameters of the gelator as a guide (30–32). Although large number of LMOGs have been investigated (e.g., steroids, ureas, peptides, saccharides), a fundamental understanding of the molecular self-assembly and gelation processes is still limited (33, 34). For example, the structural requirements for small molecules to gel a liquid are still unclear. It is recognized that assembly often involves a combination of directional interactions leading to chain structure formation and lateral isotropic van der Waals interactions between chains that lead to the formation of bundles of chains. Correlative expressions have been found useful for gel forming ability based on measures of the solvent and gelator-solvent cohesive interaction (31, 32, 34). However, despite numerous chemical and physical studies have been made on many LMOG gels, important questions remain unanswered (35–42). The early stages of fiber formation are particularly unclear. Further research is needed to better understand what molecular factors govern the strikingly regular diameter of self-assembled fibers, the thermodynamic nature of the assembly transition, the frequency of fiber branching, the effect of the solvent and inherent molecular properties that influence the propensity of formation and stability of LMOG fiber gels (43). There is also a need to better understand how fiber formation influences the viscoelastic properties of solutions in the course of the gelation process.
Modeling There is a long history of modeling electrolyte and polyelectrolyte solutions starting from the seminal analytic theory of Debye and Huckel on electrolyte solutions (44) and its extension to polymers by Manning (45, 46). These works introduced the concept of screening of ionic interactions and charge condensation of counterions on the chain backbone. Many recent modeling works have been based on Monte Carlo (47–49) and molecular dynamics simulations (50, 51) where the ions are described as charged spheres and polyelectrolytes are modeled as chains of hard spheres dispersed within a continuum background fluid having a constant dielectric constant. Molecular dynamics simulations have been performed on networks of polyelectrolyte chains based on this type of ‘restricted primitive model’ of ionic solutions (52). These studies have given important insights into the coupling of charge interactions of the polymer segments with the counter-ions and the ions of the added salt. Despite all efforts, it is apparent that many aspects of polyelectrolyte solutions are not well understood such as how simple salts affect the viscosity of the solutions (53), how basic thermodynamic properties (density, surface tension, isothermal compressibility) depend on the salt concentration, and why highly 9 Horkay et al.; Gels and Other Soft Amorphous Solids ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
charged polyelectrolytes aggregate in solution, as directly observed by small angle neutron scattering and optical microscopy (54). Recent experimental (55) and computational studies (56, 57) have suggested that many of these problems can be traced to the importance of ion, interfacial and polymer hydration, etc. These studies have confirmed that ion and polymer solvation leads to qualitatively new effects such as the emergence of long range attractive interactions between highly charged polymer chains and ion-specific changes in the viscosity and water diffusion coefficient of aqueous salt solutions even without the polyelectrolyte. We may expect that this type of modeling will provide new insights into specific ion effects typical of polyelectrolyte solutions and gels in the future based on a more realistic treatment of solvation on the properties of electrolyte and polyelectrolyte solutions. Advances in high performance computation make this type of simulation possible since a significant part of the computation involves the treatment of the solvent which was neglected in former theoretical and computational studies. The development of analytical methods for treating solvation effects in ionic solutions and polyelectrolyte solutions provides a significant challenge for the future.
Summary The physics and chemistry of polymer gels is a rapidly developing field owing to the significance of these materials in both medical and materials science. However, there are still many challenging problems that should be addressed in the future in order to rationally design materials of this kind and to understand their properties from a more fundamental perspective. In this chapter, we briefly discussed some defining features of gels and brief taxonomy of the different kinds of gels. It is expected that synergetic advances in both theory and the development of new experimental methods will lead to deeper understanding of this ubiquitous form of soft matter to enable new avenues to design for novel materials with tailored physical and chemical properties and biological function.
Acknowledgments This work was supported by the Intramural Research Program of the NICHD, NIH.
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