Kinetics of swelling of gels
01 Feb 1979-Journal of Chemical Physics (American Institute of Physics)-Vol. 70, Iss: 3, pp 1214-1218
TL;DR: In this article, a theory of the kinetics of the swelling of polyacrylamide gels is presented, which is based on the assumption that the swelling time is determined by the diffusion coefficient of the fluid molecules.
Abstract: We present a theory of the kinetics of the swelling of a gel. The characteristic time of swelling is proportional to the square of a linear dimension of the gel and is also proportional to the diffusion coefficient of the gel network, which is defined as D=E/f where E is the longitudinal bulk modulus of the network, and f is the coefficient of friction between the network and the gel fluid. This constitutes an essential difference between the present theory and the previous theory which is based on the assumption that the swelling time is determined by the diffusion coefficient of the fluid molecules. Experimental data are shown for spheres of 5% polyacrylamide gels and are analyzed using the present theory. The value of the diffusion coefficient obtained from the macroscopic swelling experiments shows excellent agreement with that obtained microscopically using laser light scattering spectroscopy.
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Wageningen University and Research Centre1, University of Cambridge2, North Carolina State University3, University of Göttingen4, Cornell University5, Leibniz Institute for Neurobiology6, Queen Mary University of London7, Northwestern University8, Georgia Institute of Technology9, University of Southern Mississippi10, Université de Montréal11, Duke University12, Clemson University13, Clarkson University14
TL;DR: This work reviews recent advances and challenges in the developments towards applications of stimuli-responsive polymeric materials that are self-assembled from nanostructured building blocks and provides a critical outline of emerging developments.
Abstract: Responsive polymer materials can adapt to surrounding environments, regulate transport of ions and molecules, change wettability and adhesion of different species on external stimuli, or convert chemical and biochemical signals into optical, electrical, thermal and mechanical signals, and vice versa. These materials are playing an increasingly important part in a diverse range of applications, such as drug delivery, diagnostics, tissue engineering and 'smart' optical systems, as well as biosensors, microelectromechanical systems, coatings and textiles. We review recent advances and challenges in the developments towards applications of stimuli-responsive polymeric materials that are self-assembled from nanostructured building blocks. We also provide a critical outline of emerging developments.
4,908 citations
TL;DR: The preparation of a material that changes colour in response to a chemical signal by means of a change in diffraction (rather than absorption) properties is reported, anticipating that this strategy can be used to prepare ‘intelligent’ materials responsive to a wide range of analytes, including viruses.
Abstract: Chemical sensors respond to the presence of a specific analyte in a variety of ways. One of the most convenient is a change in optical properties, and in particular a visually perceptible colour change. Here we report the preparation of a material that changes colour in response to a chemical signal by means of a change in diffraction (rather than absorption) properties. Our material is a crystalline colloidal array of polymer spheres (roughly 100 nm diameter) polymerized within a hydrogel that swells and shrinks reversibly in the presence of certain analytes (here metal ions and glucose). The crystalline colloidal array diffracts light at (visible) wavelengths determined by the lattice spacing, which gives rise to an intense colour. The hydrogel contains either a molecular-recognition group that binds the analyte selectively (crown ethers for metal ions), or a molecular-recognition agent that reacts with the analyte selectively. These recognition events cause the gel to swell owing to an increased osmotic pressure, which increases the mean separation between the colloidal spheres and so shifts the Bragg peak of the diffracted light to longer wavelengths. We anticipate that this strategy can be used to prepare 'intelligent' materials responsive to a wide range of analytes, including viruses.
1,861 citations
TL;DR: In this paper, a crosslinked polymeric hydrogel with grafted side chains was used to induce rapid de-swelling by tailoring the polymeric gel architecture at the molecular level.
Abstract: MANY polymeric hydrogels undergo abrupt changes in volume in response to external stimuli such as changes in solvent composition1, pH2, electric field3 and temperature4–6. For several of the potential applications of these materials, such as 'smart' actuators, a fast response is needed. The kinetics of swelling and de-swelling in these gels are typically governed by diffusion-limited transport of the polymeric components of the network in water, the rate of which is inversely proportional to the square of the smallest dimension of the gel7–9. Several strategies have been explored for increasing the response dynamics10–14, such as introducing porosity14. Here we show that we can induce rapid de-swelling of a polymer hydrogel by tailoring the gel architecture at the molecular level. We prepare a crosslinked hydrogel in which the polymer chains bear grafted side chains; the latter create hydrophobic regions, aiding the expulsion of water from the network during collapse. Whereas similar gels lacking the grafted side chains can take more than a month to undergo full de-swelling, our materials collapse in about 20 minutes.
1,161 citations
TL;DR: In this article, the phase transition of gels induced by visible light is reported, where the transition mechanism is due only to direct heating of the network polymers by light, which is an extremely fast process.
Abstract: PHASE transitions and critical phenomena in polymer gels have attracted much attention because of their scientific interest and technological significance1–3. Phase transitions accompanied by a reversible, discontinuous volume change as large as several hundred times, in response to infinitesimal changes in environmental conditions, have been observed universally in gels made of synthetic and natural polymers1–9. Phase transitions have been induced in gels by varying temperature, solvent composition, pH, ionic composition and a small electric field10. Recently, gels sensitive to ultraviolet light were also reported11. The ultraviolet light initiates an ionization reaction in the gel, creating internal osmotic pressure which induces swelling. In the absence of this light, the equilibrium tends towards the neutral polymer system and the gel collapses. This transition process is slow, as it depends on the photochemical ionization and subsequent recombination of ions, and it is technologically desirable that the transition be induced by faster mechanisms. Also, visible light is less harmful and more abundant than ultraviolet in sunlight. Hence we now report the phase transition of gels induced by visible light, where the transition mechanism is due only to the direct heating of the network polymers by light, which is an extremely fast process. Such systems might be used as photoresponsive artificial muscles, switches and memory devices.
978 citations
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TL;DR: In this paper, the authors examined the forces that produce shrinkage and the mechanisms responsible for transport of liquid, and a variety of strategies for avoiding fracture during drying were discussed, with the emphasis on the constant rate period (CRP) when the pores are full of liquid.
Abstract: This review examines the stages of drying, with the emphasis on the constant rate period (CRP), when the pores are full of liquid. It is during the CRP that most of the shrinkage occurs and the drying stresses rise to a maximum. We examine the forces that produce shrinkage and the mechanisms responsible for transport of liquid. By analyzing the interplay of fluid flow and shrinkage of the solid network, it is possible to calculate the pressure distribution in the liquid in the pores. The tension in the liquid is found to be greatest near the drying surface, resulting in greater compressive stresses on the network in that region. This produces differential shrinkage of the solid, which is the cause of cracking during drying. The probability of fracture is related to the size of the body, the rate of evaporation, and the strength of the network. A variety of strategies for avoiding fracture during drying are discussed.
977 citations
References
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TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Abstract: A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.
7,090 citations
TL;DR: In this paper, the spectrum of light scattered from thermally excited displacement fluctuations in polyacrylamide gels was measured using optical mixing spectroscopy, and the correlation function for the displacements having wave vector q is predicted for these gels to have the form of an exponential decay: exp(− Γt).
Abstract: We report measurements of the spectrum of light scattered from thermally excited displacement fluctuations in polyacrylamide gels. These measurements have been carried out on the polarized scattered light as a function of scattering angle and temperature for 5% and 2.5% polyacrylamide gels using the methods of optical mixing spectroscopy. We also present a theory for the amplitude and time dependence of the thermally excited longitudinal and transverse displacements of the gel fiber network. These displacements are responsible, respectively, for the polarized and depolarized scattered light. The correlation function for the displacements having wave vector q is predicted for these gels to have the form of an exponential decay: exp(− Γt). The decay rate is given by Γ = Glq2/f or Gtq2/f, where f is the frictional force per unit volume on the fiber network as it moves with unit velocity relative to the gel liquid. Gl is the longitudinal compressional modulus for longitudinal displacements and Gt is the shear...
655 citations
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