Colloid dynamics in semiflexible polymer solutions

Diffusing Wave Microrheology in Polymeric Fluids

Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly turbid fluids containing optical probe particles. The DWS spectrum is used to infer the time-dependent mean-square displacement and time-dependent diffusion coefficient D of the probes. From D, values for the storage modulus G'(ω) and the loss modulus G''(ω) are obtained. This paper is primarily concerned with the inference of the mean-square displacement from a DWS spectrum. However, in much of the literature, central to the inference that is said to yield D is an invocation g(1)(t)=exp(-2q2X(t)2¯) of the Gaussian Approximation for the field correlation function g(1)(t) of the scattered light in terms of the mean-square displacement X(t)2¯ of a probe particle during time t. Experiment and simulation both show that the Gaussian approximation is invalid for probes in polymeric liquids and other complex fluids. In this paper, we obtain corrections to the Gaussian approximation that will assist in interpreting DWS spectra of probes in polymeric liquids. The corrections reveal that these DWS spectra receive contributions from higher moments X(t)2n¯, n>1, of the probe displacement distribution function.

CO2-responsive gels

CO₂-responsive materials undergo a change in chemical or physical properties in response to the introduction or removal of CO₂. The use of CO₂ as a stimulus is advantageous as it is abundant, benign, inexpensive, and it does not accumulate in a system. Many CO₂-responsive materials have already been explored including polymers, latexes, surfactants, and catalysts. As a sub-set of CO₂-responsive polymers, the study of CO₂-responsive gels (insoluble, cross-linked polymers) is a unique discipline due to the unique set of changes in the gels brought about by CO₂ such as swelling or a transformed morphology. In the past 15 years, CO₂-responsive gels and self-assembled gels have been investigated for a variety of emerging potential applications, reported in 90 peer-reviewed publications. The two most widely exploited properties include the control of flow (fluids) via CO₂-triggered aggregation and their capacity for reversible CO₂ absorption-desorption, leading to applications in Enhanced Oil Recovery (EOR) and CO₂ sequestration, respectively. In this paper, we review the preparation, properties, and applications of these CO₂-responsive gels, broadly classified by particle size as nanogels, microgels, aerogels, and macrogels. We have included a section on CO₂-induced self-assembled gels (including poly(ionic liquid) gels).

Passive and Active Microrheology for Biomedical Systems

Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

Microrheology for biomaterial design

Microrheology analyzes the microscopic behavior of complex materials by measuring the diffusion and transport of embedded particle probes. This experimental method can provide valuable insight into the design of biomaterials with the ability to connect material properties and biological responses to polymer-scale dynamics and interactions. In this review, we discuss how microrheology can be harnessed as a characterization method complementary to standard techniques in biomaterial design. We begin by introducing the core principles and instruments used to perform microrheology. We then review previous studies that incorporate microrheology in their design process and highlight biomedical applications that have been supported by this approach. Overall, this review provides rationale and practical guidance for the utilization of microrheological analysis to engineer novel biomaterials.

Isomeric control of the mechanical properties of supramolecular filament hydrogels

Supramolecular filament hydrogels are an emerging class of biomaterials that hold great promise for regenerative medicine, tissue engineering, and drug delivery. The use of isomeric hydrocarbons in the peptide design enables fine-tuning of the mechanical properties of their supramolecular filament hydrogels without altering their network structures.

Effects of finite and discrete sampling and blur on microrheology experiments

The frequency-dependent viscous and elastic properties of fluids can be determined from measurements of the thermal fluctuations of a micron-sized particle trapped by optical tweezers. Finite bandwidth and other instrument limitations lead to systematic errors in measurement of the fluctuations. In this work, we numerically represented power spectra of bead position measurements as if collected by two different measurement devices: a quadrant photodiode, which measures the deflection of the trapping laser; and a high-speed camera, which images the trapped bead directly. We explored the effects of aliasing, camera blur, sampling frequency, and measurement time. By comparing the power spectrum, complex response function, and the complex shear modulus with the ideal values, we found that the viscous and elastic properties inferred from the data are affected by the instrument limitations of each device. We discuss how these systematic effects might affect experimental results from microrheology measurements and suggest approaches to reduce discrepancies.

Molecular, Local, and Network-Level Basis for the Enhanced Stiffness of Hydrogel Networks Formed from Coassembled Racemic Peptides: Predictions from Pauling and Corey

Hydrogels prepared from self-assembling peptides are promising materials for medical applications, and using both l- and d-peptide isomers in a gel's formulation provides an intuitive way to control the proteolytic degradation of an implanted material. In the course of developing gels for delivery applications, we discovered that a racemic mixture of the mirror-image β-hairpin peptides, named MAX1 and DMAX1, provides a fibrillar hydrogel that is four times more rigid than gels formed by either peptide alone-a puzzling observation. Herein, we use transmission electron microscopy, small angle neutron scattering, solid state NMR, diffusing wave, infrared, and fluorescence spectroscopies, and modeling to determine the molecular basis for the increased mechanical rigidity of the racemic gel. We find that enantiomeric peptides coassemble in an alternating fashion along the fibril long axis, forming an extended heterochiral pleat-like β-sheet, a structure predicted by Pauling and Corey in 1953. Hydrogen bonding between enantiomers within the sheet dictates the placement of hydrophobic valine side chains in the fibrils' dry interior in a manner that allows the formation of nested hydrophobic interactions between enantiomers, interactions not accessible within enantiomerically pure fibrils. Importantly, this unique molecular arrangement of valine side chains maximizes inter-residue contacts within the core of the fibrils resulting in their local stiffening, which in turn, gives rise to the significant increase in bulk mechanical rigidity observed for the racemic hydrogel.

Brownian motion of optically anisotropic spherical particles in polymeric suspensions

We studied the rotational and translational diffusion of optically anisotropic liquid crystal particles embedded in semidiluted polymer solutions of Poly-Ethylene-Oxide (PEO) at different concentrations and different molecular weights. The polymer radius of gyration was chosen to be similar to the size of the probe particles and the polymer concentrations used are just above the crossover concentration. Thus, the system consists of solid probe particles moving in a sea of overlapping particles of similar size. We found that the behavior of both particle dynamics, rotational and translational, is similar in the range of concentrations considered here. In both cases, two linear diffusive regimes are observed, separated by a subdiffusive time interval. The spatial scale at which this intermediate regime appears shows a dependence on both the polymer concentration and molecular weight, and has a value similar to the thickness of the polymer-depleted layer usually found in this kind of systems. Additionally, we observe that the colloidal dynamic scales with the overlapping degree of the polymer particles.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells. Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process. The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution. In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz. We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample. By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase. Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process. These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering.

Surface adsorption and hopping cause probe-size-dependent microrheology of actin networks

A network of filaments formed primarily by the abundant cytoskeletal protein actin gives animal cells their shape and elasticity. The rheological properties of reconstituted actin networks have been studied by tracking micron-sized probe beads embedded within the networks. We investigate how microrheology depends on surface properties of probe particles by varying the stickiness of their surface. For this purpose, we chose carboxylate polystyrene (PS) beads, silica beads, bovine serum albumin (BSA) -coated PS beads, and polyethylene glycol (PEG) -grafted PS beads, which show descending stickiness to actin filaments, characterized by confocal imaging and microrheology. Probe size dependence of microrheology is observed for all four types of beads. For the slippery PEG beads, particle-tracking microrheology detects weaker networks using smaller beads, which tend to diffuse through the network by hopping from one confinement "cage" to another. This trend is reversed for the other three types of beads, for which microrheology measures stiffer networks for smaller beads due to physisorption of nearby filaments to the bead surface. We explain the probe size dependence with two simple models. We also evaluate depletion effect near nonadsorption bead surface using quantitative image analysis and discuss the possible impact of depletion on microrheology. Analysis of these effects is necessary in order to accurately define the actin network rheology both in vitro and in vivo.

Equilibrium characteristics of semiflexible polymer solutions near probe particles

We present a numerical analysis of the mean-field theory for the structure of semiflexible polymer solutions near spherical surfaces, and use the framework to study the depletion characteristics of semiflexible polymers near colloids and nanoparticles. Our results suggest that the depletion characteristics depend sensitively on the polymer concentrations, the persistence lengths, and the radius of the particles. Broadly, two categories of features are identified based on the relative ratios of the persistence lengths to the correlation length of the polymer solution. For the limit where the correlation length is larger than the persistence length, the correlation length proves to be the critical length scale governing both the depletion thickness and the curvature effects. In contrast, for the opposite limit, the depletion thickness and the curvature effects are dependent on a length scale determined by an interplay between the persistence length and the correlation length. This leads to nontrivial (numerical) scaling laws governing the concentration and radii dependence of the depletion thicknesses. Our study also highlights the manner by which the preceding features rationalize the parametric dependencies of insertion free energies of small probes in semiflexible polymer solutions.

Brownian particles in transient polymer networks

We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings.