Diffusion in polymer solutions studied by fluorescence correlation spectroscopy

Understanding associative polymer self-assembly with shrinking gate fluorescence correlation spectroscopy

The self-assembly of polymers is integral to their role in liquid formulations. In this study, we combine a dye whose lifetime is sensitive to the nanoviscosity of its local environment with shrinking gate fluorescence correlation spectroscopy (sgFCS) to study the self-assembly of a model telechelic polymer, hydrophobically modified ethoxylated urethane (HEUR). Fluorescence lifetime measurements show a monotonic increase in average lifetime with increasing HEUR concentration driven by a small fraction of dye (<1%) with long lifetimes strongly bound to HEUR. Despite this small fraction, sgFCS isolates the diffusional dynamics of the bound fraction with no a priori assumptions as to the distribution of lifetimes. Sensitivity is greatly enhanced compared to standard FCS, revealing micellar aggregates forming between 0.2 and 1 wt% followed by formation of a percolated network. This sgFCS approach, which we apply for the first time to polymers in this work, is readily extendable to any dye that changes lifetime on binding.

Single-Molecule Tracking of Reagent Diffusion during Chemical Reactions

Recent experiments have shown that the diffusion of reagent molecules is inconsistent with what the Stokes-Einstein equation predicts during a chemical reaction. Here, we used single-molecule tracking to observe the diffusion of reactive reagent molecules during click and Diels-Alder (DA) reactions. We found that the diffusion coefficient of the reagents remained unchanged within the experimental uncertainty upon the DA reaction. Yet, diffusion of reagent molecules is faster than predicted during the click reaction when the reagent concentration and catalyst concentration exceed a threshold. A stepwise analysis suggested that the fast diffusion scenario is due to the reaction but not the involvement of the tracer with the reaction itself. The present results provide experimental evidence on the faster-than-expected reagent diffusion during a CuAAC reaction in specific conditions and propose new insights into understanding this unexpected behavior.

Molecular Dynamics Simulations of Rhodamine B Zwitterion Diffusion in Polyelectrolyte Solutions

Polyelectrolytes continue to find wide interest and application in science and engineering, including areas such as water purification, drug delivery, and multilayer thin films. We have been interested in the dynamics of small molecules in a variety of polyelectrolyte (PE) environments; in this paper, we report simulations and analysis of the small dye molecule rhodamine B (RB) in several very simple polyelectrolyte solutions. Translational diffusion of the RB zwitterion has been measured in fully atomistic, 2 μs long molecular dynamics simulations in four different polyelectrolyte solutions. Two solutions contain the common polyanion sodium poly(styrene sulfonate) (PSS), one with a 30-mer chain and the other with 10 trimers. The other two solutions contain the common polycation poly(allyldimethylammonium) chloride (PDDA), one with two 15-mers and the other with 10 trimers. RB diffusion was also simulated in several polymer-free solutions to verify its known experimental value for the translational diffusion coefficient, D_RB, of 4.7 × 10^-6 cm²/s at 300 K. RB diffusion was slowed in all four simulated PE solutions, but to varying degrees. D_RB values of 3.07 × 10^-6 and 3.22 × 10^-6 cm²/s were found in PSS 30-mer and PSS trimer solutions, respectively, whereas PDDA 15-mer and trimer solutions yielded values of 2.19 × 10^-6 and 3.34 × 10^-6 cm²/s. Significant associations between RB and the PEs were analyzed and interpreted via a two-state diffusion model (bound and free diffusion) that describes the data well. Crowder size effects and anomalous diffusion were also analyzed. Finally, RB translation along the polyelectrolytes during association was characterized.

Effect of PEGylation on the Drug Release Performance and Hemocompatibility of Photoresponsive Drug-Loading Platform

Coronary stenosis has been one of the most common heart diseases that drastically increases the risk of fatal disorders such as heart attack. Angioplasty using drug coated balloons (DCB) has been one of the most safe and promising treatments. To minimize the risk of thrombosis of such DCBs during intervention, a different approach that can secure high hemocompatibility under blood flow is necessary. Here we report a method of improving the photoresponsive platform's hemocompatibility by conjugating polyethylene glycol (PEG), onto the functional groups located at the balloon surface. In this study, latex microbeads were used as models for balloons to enable precise observation of its surface under microscopy. These beads were decorated with PEG polymers of a variety of lengths and grafting densities, along with the Cy5-Photoclevable (PC) linker conjugate to mimic drugs to be loaded onto the platform. Results showed that PEG length and grafting density are both critical factors that alter not only its hemocompatibility, but also the drug load and release efficiency of such platform. Thus, although further investigation is necessary to optimize the tradeoff between hemocompatibility, drug load, and release efficiency, it is safe to conclude that PEGylation of DCB surface is an effective method of enhancing and maintaining high hemocompatibility to minimize the risk of thrombosis during angioplasty.

Molecular diffusion in ternary poly(vinyl alcohol) solutions

The diffusion kinetics of a molecular probe—rhodamine B—in ternary aqueous solutions containing poly(vinyl alcohol), glycerol, and surfactants was investigated using fluorescence correlation spectroscopy and dynamic light scattering. We show that the diffusion characteristics of rhodamine B in such complex systems is determined by a synergistic effect of molecular crowding and intermolecular interactions between chemical species. The presence of glycerol has no noticeable impact on rhodamine B diffusion at low concentration, but significantly slows down the diffusion of rhodamine B above 3.9% (w/v) due to a dominating steric inhibition effect. Furthermore, introducing surfactants (cationic/nonionic/anionic) to the system results in a decreased diffusion coefficient of the molecular probe. In solutions containing nonionic surfactant, this can be explained by an increased crowding effect. For ternary poly(vinyl alcohol) solutions containing cationic or anionic surfactant, surfactant—polymer and surfactant—rhodamine B interactions alongside the crowding effect of the molecules slow down the overall diffusivity of rhodamine B. The results advance our insight of molecular migration in a broad range of industrial complex formulations that incorporate multiple compounds, and highlight the importance of selecting the appropriate additives and surfactants in formulated products.

Macroscopic Viscosity of Polymer Solutions from the Nanoscale Analysis

The effective viscosity in polymer solutions probed by diffusion of nanoparticles depends on their size. It is a well-defined function of the probe size, the radius of gyration, mesh size (correlation length), activation energy, and its parameters. As the nanoparticle's size exceeds the radius of gyration of polymer coils, the effective viscosity approaches its macroscopic limiting value. Here, we apply the equation for effective viscosity in the macroscopic limit to the following polymer solutions: hydroxypropyl cellulose (HPC) in water, polymethylmethacrylate (PMMA) in toluene, and polyacrylonitrile (PAN) in dimethyl sulfoxide (DMSO). We compare them with previous data for PEG/PEO in water and PDMS in ethyl acetate. We determine polymer parameters from the measurements of the macroscopic viscosity in a wide range of average polymer molecular weights (24-300 kg/mol), temperatures (283-303 K), and concentrations (0.005-1.000 g/cm³). In addition, the polydispersity of polymers is taken into account in the appropriate molecular weight averaging functions. We provide the model applicable for the study of nanoscale probe diffusion in polymer solutions and macroscopic characterization of different polymer materials via rheological measurements.

Simulation on diffusivity and statistical size of polymer chains in polymer nanocomposites

The dynamical and conformational properties of polymer chains are affected significantly by strongly attractive nanoparticles. The adsorption of polymer chains on nanoparticles not only reduces the dynamics but also changes the conformation of polymer chains. For orderly distributed nanoparticles of size roughly the same as the radius of gyration of polymer chains, the variation of the diffusivity is highly related to that of the statistical size and can be explained mainly from the adsorption of polymers. In particular, both the polymer's size and diffusivity reach the minimum when the number of polymer chains matches the number of nanoparticles where polymer chains are mostly adsorbed on separate nanoparticles. The behavior of diffusivity can be explained from the cooperation of polymer adsorption and nanoparticle-exchange motion. Adsorption of the polymer chain slows down the diffusion, whereas the nanoparticle-exchange motion accelerates the diffusion of polymer chains.

How Tethered Probes Report the Dynamics of a Polymer near the Glass Transition

How tethered probes report dynamics of host polymers near the glass transition was investigated by changing the length of the flexible linkers and the number of tethering points via imaging rotational fluorescence correlation microscopy and compared with free probes of different sizes. The results show that tethering did not alter the temperature-dependence of polymer dynamics and the shape of the correlation decay reported by the probe; however, the rotation slowed down up to ≈1 decade when both ends of the probe were restricted with short alkyl chain linkers. Upon comparison with the bigger free probe, the mechanism of the slowdown was attributed to the restricted motion upon tethering for tethered probes compared to averaging over different regions of the dynamic heterogeneity for the bigger probe. If the size of the probe was comparable to that of the dynamic heterogeneity of the system, tethered probes accurately report dynamics relevant to glass transition, regardless of tethering conditions.

Particle Diffusion in Polymeric Hydrogels with Mixed Attractive and Repulsive Interactions

All biogels are heterogeneous, consisting of functional groups with different biophysical properties arrayed on spatially disordered polymer networks. Nanoparticles diffusing in such biogels experience a mixture of attractive and repulsive interactions. Here, we present experimental and theoretical studies of charged particle diffusion in gels with a random distribution of attractive and repulsive electrostatic interaction sites inside the gel. In addition to interaction disorder, we theoretically investigate the effect of spatial disorder of the polymer network. Our coarse-grained simulations reveal that attractive interactions primarily determine the diffusive behavior of the particles in systems with mixed attractive and repulsive interactions. As a consequence, charged particles of either sign are immobilized in mixed cationic/anionic gels because they are trapped near oppositely charged interaction sites, whereas neutral particles diffuse rapidly. Even small fractions of oppositely charged interaction sites lead to strong trapping of a charged particle. Translational diffusion coefficients of charged probe molecules in gels consisting of mixed cationic and anionic dextran polymers are determined by fluorescence correlation spectroscopy and quantitatively confirm our theoretical predictions.

Transition from double to single diffusive behavior with increase in polymer concentration for oppositely charged guest - host systems of green fluorescent protein diffusing inside poly-l-lysine solutions

The effect of crowding, background and probe charges and chain flexibility on probe dynamics of Green Fluorescent Protein in polyelectrolyte solutions of poly-l-lysine was investigated using Fluorescence Recovery After Photobleaching (FRAP). An interesting double diffusive behavior in FRAP recovery curve was observed at low polymer concentration resulting in two relaxation modes, which disappears with rise in polymer concentration. The fast relaxation mode attributes to diffusion of free protein molecules alone, where as slow mode is credited to polymer adsorbed protein molecules. Absence of double diffusive behavior at higher polymer concentration is argued in terms of varying host chain conformation and the only relaxation mode present is due to movement of free probes alone rather than that of adsorbed proteins. We noticed only a marginal decrease in diffusion coefficient with rise in salt concentration and the trend is reversed when variation in sample viscosity with salt is taken into account. In addition a small but systematic decrease in diffusion coefficient is seen with increase in magnitude of probe charge. Comparison of results with ideal Stoke - Einstein relation brings out the importance of polyelectrolyte effect and indicates ∼200 - fold positive deviations from predicted value for both variation in ionic strength and solution pH.

Motion of nanoprobes in complex liquids within the framework of the length-scale dependent viscosity model

This paper deals with the recent phenomenological model of the motion of nanoscopic objects (colloidal particles, proteins, nanoparticles, molecules) in complex liquids. We analysed motion in polymer, micellar, colloidal and protein solutions and the cytoplasm of living cells using the length-scale dependent viscosity model. Viscosity monotonically approaches macroscopic viscosity as the size of the object increases and thus gives a single, coherent picture of motion at the nano and macro scale. The model includes interparticle interactions (solvent-solute), temperature and the internal structure of a complex liquid. The depletion layer ubiquitously occurring in complex liquids is also incorporated into the model. We also discuss the biological aspects of crowding in terms of the length-scale dependent viscosity model.

Accurate Diffusion Coefficients of Organosoluble Reference Dyes in Organic Media Measured by Dual-Focus Fluorescence Correlation Spectroscopy

Dual-focus fluorescence correlation spectroscopy (2fFCS) is a versatile method to determine accurate diffusion coefficients of fluorescent species in an absolute, reference-free manner. Whereas (either classical or dual-focus) FCS has been employed primarily in the life sciences and thus in aqueous environments, it is increasingly being used in materials chemistry, as well. These measurements are often performed in nonaqueous media such as organic solvents. However, the diffusion coefficients of reference dyes in organic solvents are not readily available. For this reason we determined the translational diffusion coefficients of several commercially available organosoluble fluorescent dyes by means of 2fFCS. The selected dyes and organic solvents span the visible spectrum and a broad range of refractive indices, respectively. The diffusion coefficients can be used as absolute reference values for the calibration of experimental FCS setups, allowing quantitative measurements to be performed. We show that reliable information about the hydrodynamic dimensions of the fluorescent species (including noncommercial compounds) within organic media can be extracted from the 2fFCS data.

Oil diffusivity through fat crystal networks

Oil migration in chocolate and chocolate-based confections leads to undesirable visual and textural changes. Establishing ways to slow this unavoidable process would increase shelf life and reduce consumer rejection. Diffusion is most often credited as the main pathway by which oil migration occurs. Here, we use fluorescence recovery after photobleaching (FRAP) to explore the diffusion coefficients of vegetable and mineral oil through fat crystal networks at different solid fat contents (SFC). Differences in compatibility between the fat and oil lead to unique primary crystal clusters, yet those variations do not affect diffusion at low SFCs. Trends deviate at higher SFCs, which we ascribe to the influence of the differing crystal cluster structures. We relate our results to the strong and weak-link rheological regimes of fat crystal networks. Finally, we connect the results to relationships developed for polymer gel systems.

Optical tracking of anomalous diffusion kinetics in polymer microspheres

In this Letter we propose the use of whispering gallery mode resonance tracking as a label-free optical means to monitor diffusion kinetics in glassy polymer microspheres. Approximate solutions to the governing diffusion equations are derived for the case of slow relaxation and small Stefan number. Transduction of physical changes in the polymer, including formation of a rubbery layer, swelling, and dissolution, into detectable resonance shifts are described using a perturbative approach. Concrete examples of poly(methyl methacrylate) and polystyrene spheres in water are considered.

Molecular structure effects on the post irradiation diffusion in polymer gel dosimeters

Polymer gel dosimeters have specific advantages for recording 3D radiation dose distribution in diagnostic and therapeutic medical applications. But, even in systems where the 3D structure is usually maintained for long periods of time after irradiation, it is still not possible to eliminate the diffusion of the different species in the regions of dose gradients within the gel. As a consequence, information of the dose loses quality over time. In the pursuit of a solution and to improve the understanding of this phenomenon a novel system based on itaconic acid and N-N'-methylene-bisacrylamide (BIS) is hereby proposed. Effects of changes in the chemical structure of the monomers over the dosimetric sensitivity and over the post-irradiation diffusion of species was studied. In this study, one of the carboxylic groups of the itaconic acid molecule was modified with aniline to obtain molecules with similar reactivity but different molecular sizes. Then, dosimeters based on these modified species and on the original ITA molecules were irradiated in an X-ray tomography apparatus at different doses up to 173Gy. Afterwards, the resulting dosimeters were characterized by Raman spectroscopy and optical absorbance in order to study their feasibility and capabilities as dosimetric systems, and by optical-CT to analyze the post irradiation diffusion.

Fluorescence Correlation Spectroscopy in Dilute Polymer Solutions: Effects of Molar Mass Dispersity and the Type of Fluorescent Labeling

Fluorescence correlation spectroscopy (FCS) has become an important tool in polymer science. Among various other applications the method is often applied to measure the hydrodynamic radius and the degree of fluorescent labeling of polymers in dilute solutions. Here we show that such measurements can be strongly affected by the molar mass dispersity of the studied polymers and the way of labeling. As model systems we used polystyrene and poly(methyl methacrylate) synthesized by atom transfer radical polymerization or free-radical polymerization. Thus, the polymers were either end-labeled bearing one fluorophore per chain or side-labeled with a number of fluorophores per chain proportional to the degree of polymerization.The experimentally measured autocorrelation curves were fitted with a newly derived theoretical model that uses the Schulz-Zimm distribution function to describe the dispersity in the degree of polymerization. For end-labeled polymers having a molecular weight distribution close to Schulz-Zimm, the fits yield values of the number-average degree of polymerization and the polydispersity index similar to those obtained by reference gel permeation chromatography. However, for the side-labeled polymers such fitting becomes unstable, especially for highly polydisperse systems. Brownian dynamic simulations showed that the effect is due to a mutual dependence between the fit parameters, namely, the polydispersity index and the number-average molecular weight. As a consequence, an increase of the polydispersity index can be easily misinterpreted as an increase of the molecular weight when the FCS autocorrelation curves are fitted with a standard single component model, as commonly done in the community.

Particle transport through hydrogels is charge asymmetric

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks.

Super-resolution study of polymer mobility fluctuations near c*

Nanoscale dynamic heterogeneities in synthetic polymer solutions are detected using super-resolution optical microscopy. To this end, we map concentration fluctuations in polystyrene-toluene solutions with spatial resolution below the diffraction limit, focusing on critical fluctuations near the polymer overlap concentration, c*. Two-photon super-resolution microscopy was adapted to be applicable in an organic solvent, and a home-built STED-FCS system with stimulated emission depletion (STED) was used to perform fluorescence correlation spectroscopy (FCS). The polystyrene serving as the tracer probe (670 kg mol(-1), radius of gyration RG ≈ 35 nm, end-labeled with a bodipy derivative chromophore) was dissolved in toluene at room temperature (good solvent) and mixed with matrix polystyrene (3,840 kg mol(-1), RG ≈ 97 nm, Mw/Mn = 1.04) whose concentration was varied from dilute to more than 10c*. Whereas for dilute solutions the intensity-intensity correlation function follows a single diffusion process, it splits starting at c* to imply an additional relaxation process provided that the experimental focal area does not greatly exceed the polymer blob size. We identify the slower mode as self-diffusion and the increasingly rapid mode as correlated segment fluctuations that reflect the cooperative diffusion coefficient, Dcoop. These real-space measurements find quantitative agreement between correlation lengths inferred from dynamic measurements and those from determining the limit below which diffusion coefficients are independent of spot size. This study is considered to illustrate the potential of importing into polymer science the techniques of super-resolution imaging.

Length-scale dependent transport properties of colloidal and protein solutions for prediction of crystal nucleation rates

We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 μm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or electrostatic interactions. We implement contribution of those interactions into the scaling law. Finally we use our scaling law together with the literature values of the barrier for nucleation to predict crystal nucleation rates of hard-sphere like colloids. The resulting crystal nucleation rates agree with existing experimental data.

Complex tracer diffusion dynamics in polymer solutions

We employ fluorescence correlation spectroscopy (FCS) and coarse-grained molecular dynamics simulations to study the mobility of tracers in polymer solutions. Excluded volume interactions result in crowding-induced slowdown, depending only on the polymer concentration. With specific tracer-polymer attractions, the tracer is slowed down at much lower concentrations, and a second diffusion component appears that is sensitive to the polymer chain length. The two components can be resolved by FCS, only if the distance traveled by the tracer in the polymer-bound state is greater than the FCS focal spot size. The tracer dynamics can be used as a sensitive probe of the nature and strength of interactions, which-despite their local character-emphasize the role of chain connectivity.

Tracer diffusion in a crowded cylindrical channel

Based on a coarse-grained model, we carry out molecular dynamics simulations to analyze the diffusion of a small tracer particle inside a cylindrical channel whose inner wall is covered with randomly grafted short polymeric chains. We observe an interesting transient subdiffusive behavior along the cylindrical axis at high attraction between the tracer and the chains, however, the long-time diffusion is always normal. This process is found to be enhanced for the case that we immobilize the grafted chains, i.e., the subdiffusive behavior sets in at an earlier time and spans over a longer time period before becoming diffusive. Even if the grafted chains are replaced with a frozen sea of repulsive, nonconnected particles in the background, a transient subdiffusion is observed. The intermediate subdiffusive behavior only disappears when the grafted chains are replaced with a mobile background sea of mutually repulsive particles. Overall, the long-time diffusion coefficient of the tracer along the cylinder axis decreases with an increase in system volume fraction, the strength of the attraction between the tracer and the background, and also on freezing the background.

Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation

Dual color fluorescence cross-correlation spectroscopy (DC FCCS) experiments were conducted to study the coalescence and aggregation during the formation of nanoparticles. To assess the generality of the method, three completely different processes were selected to prepare the nanoparticles. Polymeric nanoparticles were formed either by solvent evaporation from emulsion nanodroplets of polymer solutions or by miniemulsion polymerization. Inorganic nanocapsules were formed by polycondensation of alkoxysilanes at the interface of nanodroplets. In all cases, DC FCCS provided fast and unambiguous information about the occurrence of coalescence and thus a deeper insight into the mechanism of nanoparticle formation. In particular, it was found that coalescence played a minor role for the emulsion-solvent evaporation process and the miniemulsion polymerization, whereas substantial coalescence was detected during the formation of the inorganic nanocapsules. These findings demonstrate that DC FCCS is a powerful tool for monitoring nanoparticles genesis.

Confined diffusion in periodic porous nanostructures

We performed fluorescence correlation spectroscopy measurements to assess the long-time self-diffusion of a variety of spherical tracer particles in periodic porous nanostructures. Inverse opal structures with variable cavity sizes and openings in the nanometer domain were employed as the model system. We obtained both the exponent of the scaling relation between mean-square displacement and time and the slow-down factors due to the periodic confinement for a number of particle sizes and confining characteristics. In addition, we carried out Brownian dynamics simulations to model the experimental conditions. Good agreement between experimental and simulation results has been obtained regarding the slow-down factor. Fickian diffusion is predicted and seen in almost all experimental systems, while apparent non-Fickian exponents that show up for two strongly confined systems are attributed to polydispersity of the cavity openings. The utility of confining periodic porous nanostructures holds promise toward understanding of constrained diffusion with a wide range of applications ranging from water purification and drug delivery to tissue engineering.