Theory and simulation of the swelling of polymer gels

On the Swelling of Polymer Network Strands

Large scale computer simulations are employed to analyze the conformations of network strands in polymer networks at preparation conditions (characterized by a polymer volume fraction of ϕ0) and when swollen to equilibrium (characterized by a polymer volume fraction ϕ < ϕ0). Network strands in end-linked model networks are weakly stretched and partially swollen at preparation conditions as compared to linear polymers in the same solvent at ϕ0. Equilibrium swelling causes non-ideal chain conformations characterized by an effective scaling exponent approaching 7/10 on intermediate length scales for increasing overlap of the chains. The chain size in a network consists of a fluctuating and a time average "elastic" contribution. The elastic contribution swells essentially affinely ∝(ϕ0/ϕ)2/3, whereas the swelling of the fluctuating part lies between the expected swelling of the entanglement constraints and the swelling of non-cross-linked chains in a comparable semi-dilute solution. The total swelling of chain size results from the changes of both fluctuating and non-fluctuating contributions.

Paper-Based Humidity Sensors as Promising Flexible Devices: State of the Art: Part 1. General Consideration

In the first part of the review article "General considerations" we give information about conventional flexible platforms and consider the advantages and disadvantages of paper when used in humidity sensors, both as a substrate and as a humidity-sensitive material. This consideration shows that paper, especially nanopaper, is a very promising material for the development of low-cost flexible humidity sensors suitable for a wide range of applications. Various humidity-sensitive materials suitable for use in paper-based sensors are analyzed and the humidity-sensitive characteristics of paper and other humidity-sensitive materials are compared. Various configurations of humidity sensors that can be developed on the basis of paper are considered, and a description of the mechanisms of their operation is given. Next, we discuss the manufacturing features of paper-based humidity sensors. The main attention is paid to the consideration of such problems as patterning and electrode formation. It is shown that printing technologies are the most suitable for mass production of paper-based flexible humidity sensors. At the same time, these technologies are effective both in the formation of a humidity-sensitive layer and in the manufacture of electrodes.

Polyelectrolyte Gels: A Unique Class of Soft Materials

The objective of this article is to introduce the readers to the field of polyelectrolyte gels. These materials are common in living systems and have great importance in many biomedical and industrial applications. In the first part of this paper, we briefly review some characteristic properties of polymer gels with an emphasis on the unique features of this type of soft material. Unsolved problems and possible future research directions are highlighted. In the second part, we focus on the typical behavior of polyelectrolyte gels. Many biological materials (e.g., tissues) are charged (mainly anionic) polyelectrolyte gels. Examples are shown to illustrate the effect of counter-ions on the osmotic swelling behavior and the kinetics of the swelling of model polyelectrolyte gels. These systems exhibit a volume transition as the concentration of higher valence counter-ions is gradually increased in the equilibrium bath. A hierarchy is established in the interaction strength between the cations and charged polymer molecules according to the chemical group to which the ions belong. The swelling kinetics of sodium polyacrylate hydrogels is investigated in NaCl solutions and in solutions containing both NaCl and CaCl₂. In the presence of higher valence counter-ions, the swelling/shrinking behavior of these gels is governed by the diffusion of free ions in the swollen network, the ion exchange process and the coexistence of swollen and collapsed states.

Effect of Chain Polydispersity on the Elasticity of Disordered Polymer Networks

Due to their unique structural and mechanical properties, randomly cross-linked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρinit and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same C, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by ρinit. We rationalize this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.

Droplet-train induced spatiotemporal swelling regimes in elastomers

In this work, we perform a combined experimental and numerical analysis of elastomer swelling dynamics upon impingement of a train of solvent droplets. We use time scale analysis to identify spatiotemporal regimes resulting in distinct boundary conditions that occur based on relative values of the absorption timescale and the droplet train period. We recognize that when either timescale is significantly larger than the other, two cases of quasi-uniform swelling occur. In contrast, when the two timescales are comparable, a variety of temporary geometrical features due to localized swelling are observed. We show that the swelling feature and its temporal evolution depends upon geometric scaling of polymer thickness and width relative to the droplet size. Based on this scaling, we identify six cases of localized swelling and experimentally demonstrate the swelling features for two cases representing limits of thickness and width. A finite element model of local swelling is developed and validated with experimental results for these two cases. The model is subsequently used to explore the swelling behavior in the rest of the identified cases. We show that depending upon the lateral dimension of the sample, swelling can locally exhibit mushroom, mesa, and cap like shapes. These deformations are magnified during the droplet-train impact but dissipate during post-train polymer equilibration. Our results also show that while swelling shape is a function of lateral dimensions of the sample, the extent of swelling increases with the elastomer sample thickness.

Entropy Driven Phase Transition in Polymer Gels: Mean Field Theory

We present a mean field model of a gel consisting of P polymers, each of length L and N_z polyfunctional monomers. Each polyfunctional monomer forms z covalent bonds with the 2P bifunctional monomers at the ends of the linear polymers. We find that the entropy dependence on the number of polyfunctional monomers exhibits an abrupt change at N_z = 2P/z due to the saturation of possible crosslinks. This non-analytical dependence of entropy on the number of polyfunctionals generates a first-order phase transition between two gel phases: one poor and the other rich in poly-functional molecules.

Phase separation behavior of mixed lipid systems at neutral and low pH: coarse-grained simulations with DMD/LIME

We extend LIME, an intermediate resolution, implicit solvent model for phospholipids previously used in discontinuous molecular dynamics simulations of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayer formation at 325 K, to the description of the geometry and energetics of 1,2-distearoyl-sn-glycero-3-phospho-L-serine (DSPS) and 1,2-dihenarachidoyl-sn-glycero-3-phosphocholine (21PC) and mixtures thereof at both neutral and low pH at 310 K. A multiscale modeling approach is used to calculate the LIME parameters from atomistic simulation data on a mixed DPPC/DSPS system at different pH values. In the model, 17 coarse-grained sites represent DSPS and 18 coarse-grained sites represent 21PC. Each of these coarse-grained sites is classified as 1 of 9 types. LIME/DMD simulations of equimolar bilayers show the following: (1) 21PC/DSPS bilayers with and without surface area restrictions separate faster at low pH than at neutral pH, (2) 21PC/DSPS systems separate at approximately the same rate regardless of whether they are subjected to surface area restrictions, and (3) bilayers with a molar ratio of 9:1 (21PC:DSPS) phase separate to form heterogeneous domains faster at low pH than at neutral pH. Our results are consistent with experimental findings of Sofou and co-workers (Bandekar et al. Mol. Pharmaceutics, 2013, 10, 152-160; Karve et al. Biomaterials, 2010, 31, 4409-4416) that more doxorubicin is released from 21PC/DSPS liposomes at low pH than at neutral pH, presumably because greater phase separation is achieved at low pH than at neutral pH. These are the first molecular-level simulations of the phase separation in mixed lipid bilayers induced by a change in pH.

Molecular dynamics simulations of DPPC bilayers using "LIME", a new coarse-grained model

A new intermediate resolution model for phospholipids, LIME, designed for use with discontinuous molecular dynamics (DMD) simulations is presented. The implicit-solvent model was developed using a multiscale modeling approach in which the geometric and energetic parameters are obtained by collecting data from atomistic simulations of a system composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules and explicit water. In the model, 14 coarse-grained sites that are classified as 1 of 6 types represent DPPC. DMD simulations performed on a random solution of DPPC resulted in the formation of a defect-free bilayer in less than 4 h. The bilayer formed quantitatively reproduces the main structural properties (e.g., area per lipid, bilayer thickness, bond order parameters) that are observed experimentally. In addition, the bilayer transitions from a liquid-crystalline phase to a tilted gel phase when the temperature is reduced. Transbilayer movement of a lipid from the bottom leaflet to the top leaflet is observed when the temperature is increased.

Predicting water sorption and volume swelling in dense polymer systems via computer simulation

Atomistic model structures of amorphous polyamide 6 (PA-6) and of an adhesive system consisting of the diglycidyl ether of bisphenol A (DGEBA) as epoxy resin and isophorone diamine (IPD) as a curing agent are generated. For the adhesive, we use a new approach for the generation of the cross-linked polymer networks. It takes into account the chemical reaction kinetics of the curing reaction and, therefore, results in more realistic network structures. On the basis of the corresponding model structures, the equilibrium water content and the swelling ratio of amorphous PA-6 and of the DGEBA+IPD networks are calculated via computer simulation for different thermodynamic conditions. A hybrid method is used combining the molecular dynamics technique with an accelerated test particle insertion method. The results are in reasonable agreement with experiments and, in the case of the PA-6 system, with results obtained via other computer simulation methods.

Piezoresistive Chemosensoren auf der Basis von Hydrogelen (Piezoresistive Chemical Sensors Based on Hydrogels)

Hydrogele zeigen in Abhängigkeit von der sie umgebenden Flüssigkeit ein starkes Quellungsvermögen. Dies kann für die Schaffung chemischer Sensoren, z.B. für die Messung des pH-Wertes, ausgenutzt werden. Dafür lassen sich piezoresistive Sensoren nutzen, wobei das quellende Hydrogel zu einer Verformung der Silizium-Biegeplatte des Sensorchips führt. Es wurden die Ausgangsspannung in Abhängigkeit vom pH-Wert untersucht und die für eine hohe Signalreproduzierbarkeit erforderlichen Messbedingungen ermittelt.

Computer simulation of polymer networks: Swelling by binary Lennard-Jones mixtures

The swelling of regular, tightly meshed model networks is investigated by a molecular-dynamics-Monte Carlo hybrid technique. The chemical equilibrium between two simulation boxes representing the gel phase and a solvent bath, respectively, is obtained by subjecting the Lennard-Jones particles of a binary mixture, serving as explicit solvent, to the particle transfer step of Gibbs ensemble-Monte Carlo. The swelling behavior, especially preferential absorption of a single component, whose dependence on temperature, pressure, and fluid composition is studied, also depends significantly on the size of the central simulation cell. These finite-size effects correlate well with those exhibited by the density of solvent-free (dry) networks. A theoretical expression, whose derivation is based on network elasticity (of dry networks) yields finite-size scaling behavior in good accord with simulation results for both dry networks and gels in contact with solvent baths. This expression can be used to extrapolate the swelling behavior of simulated finite systems to infinite system size.

Swelling of model polymer networks with different cross-link densities: a computer simulation study

The swelling of model polymer networks with different cross-link densities is studied via molecular dynamics simulation. During the simulation, the solvent particles, consisting of one interaction center or six interaction centers, respectively, are transferred between two coupled simulation boxes. The gel box includes both network and solvent particles, whereas the solvent box contains solvent only. The particle transfer is controlled by the solvent chemical potential difference in the two boxes, which is calculated via the Widom test particle method for the one-site solvent and via Rosenbluth sampling for the chainlike solvent. The equilibrium swelling ratio of the network as well as the solvent diffusion coefficient under subcritical and supercritical conditions are computed as functions of the network cross-link density for a wide range of temperatures and pressures. In addition, the simulated swelling behavior is compared to a Flory-Huggins-type theory, which yields qualitative agreement for the systems studied here.

Computer simulation study on the swelling of a model polymer network by a chainlike solvent

A molecular-dynamics-particle-transfer method was used to study the swelling of a model polymer network by a short chain solvent. The solvent chains were transferred depending on the difference between the solvent chemical potentials in the coupled simulation boxes, containing pure solvent and gel, respectively. The chemical potentials were computed via the Rosenbluth sampling method. The simulated swelling ratio of the network under subcritical and supercritical conditions is compared with the prediction of a modified Flory-Huggins theory. In addition, the chains exhibit markedly different structural and dynamic properties in the corresponding phases due to the constraint imposed by the network, which are discussed in detail.

alpha-helix formation: discontinuous molecular dynamics on an intermediate-resolution protein model

An intermediate-resolution model of small, homogeneous peptides is introduced, and discontinuous molecular dynamics simulation is applied to study secondary structure formation. Physically, each model residue consists of a detailed three-bead backbone and a simplified single-bead side-chain. Excluded volume and hydrogen bond interactions are constructed with discontinuous (i.e., hard-sphere and square-well) potentials. Simulation results show that the backbone motion of the model is limited to realistic regions of Phi-Psi conformational space. Model polyalanine chains undergo a locally cooperative transition to form alpha-helices that are stabilized by backbone hydrogen bonding, while model polyglycine chains tend to adopt nonhelical structures. When side-chain size is increased beyond a critical diameter, steric interactions prevent formation of long alpha-helices. These trends in helicity as a function of residue type have been well documented by experimental, theoretical, and simulation studies and demonstrate the ability of the intermediate-resolution model developed in this work to accurately mimic realistic peptide behavior. The efficient algorithm used permits observation of the complete helix-coil transition within 15 min on a single-processor workstation, suggesting that simulations of very long times are possible with this model.

Swelling of a model polymer network by a one-site solvent: computer simulation and Flory-Huggins-like theory

A molecular-dynamics-Widom test particle-simulation was used to investigate the swelling of a model polymer network in contact with a one-site solvent under subcritical and supercritical conditions. Particle motion is computed via molecular dynamics. Simultaneously, the solvent particle concentration is controlled by direct comparison of the chemical potentials in two reference systems (pure solvent and network including solvent), which are calculated using Widom's test particle method. The simulated swelling isotherms exhibit complex behavior: at the subcritical conditions considered here, the swelling ratio decreases with increasing pressure. At the intermediate supercritical temperatures the isotherms exhibit a peak, which disappears with the elevation of temperature. At high temperatures, the swelling ratio of the network increases monotonically with increasing pressure. The corresponding isobars also exhibit a maximum, which broadens and shifts to higher temperatures with increasing supercritical pressure. These results are in qualitative agreement with the prediction of a modified Flory-Huggins theory and with the results of known experiments. Furthermore, the self-diffusion coefficients of the solvent in the network and in its pure state are simulated. The solvent mobility in the network is significantly decreased because of the hindrance of network beads, but exhibits different behavior at subcritical in comparison to supercritical temperatures.