Semidilute Solutions Research Articles

In Situ RheoNMR Correlation of Polymer Segmental Mobility with Mechanical Properties during Hydrogel Synthesis.

Understanding polymer gelation over multiple length‐scales is crucial to develop advanced materials. An experimental setup is developed that combines rheological measurements with simultaneous time‐domain 1H NMR relaxometry (TD‐NMR) techniques, which are used to study molecular motion (<10 nm) in soft matter. This so‐called low‐field RheoNMR setup is used to study the impact of varying degrees of crosslinking (DC) on the gelation kinetics of acrylic acid (AAc) and N,N′‐methylene bisacrylamide (MBA) free radical crosslinking copolymerization. A stretched exponential function describes the T 2 relaxation curves throughout the gelation process. The stretching exponent β decreases from 0.90 to 0.67 as a function of increasing DC, suggesting an increase in network heterogeneity with a broad T 2 distribution at higher DC. The inverse correlation of the elastic modulus G′ with T 2 relaxation times reveals a pronounced molecular rigidity for higher DC at early gelation times, indicating the formation of inelastic, rigid domains such as crosslinking clusters. The authors further correlate G′ with the polymer concentration during gelation using a T 1 filter for solvent suppression. A characteristic scaling exponent of 2.3 is found, which is in agreement with theoretical predictions of G′ based on the confining tube model in semi‐dilute entangled polymer solutions.

Quantifying Properties of Polysaccharide Solutions.

We apply a scaling theory of semidilute polymer solutions to quantify solution properties of polysaccharides such as galactomannan, chitosan, sodium carboxymethyl cellulose, hydroxypropyl methyl cellulose, methyl cellulose, xanthan, apple pectin, cellulose tris(phenyl carbamate), hydroxyethyl cellulose, hydroxypropyl cellulose, sodium hyaluronate, sodium alginate, and sodium κ-carrageenan. In particular, we obtain the molar mass of the chain segment inside a correlation blob M g = B̂ 3/(3ν-1) c 1/(1-3ν) as a function of concentration c, interaction parameter B̂, and exponent ν. Parameter B̂ assumes values B̂ g, B̂ th and M 0/N A 1/3 l for exponents v = 0.588, 0.5 and 1, respectively, where M 0 is the molar mass of a repeat unit, l is the projection length of a repeat unit, and N A is the Avogadro number. In the different solution regimes, the values of the B̂-parameters are extracted from the plateaus of the normalized specific viscosity ηsp (c)/M w c 1/(3ν-1), where M w is the weight-average molecular weight of the polymer chain. The values of the B̂-parameters are used in calculations of the excluded volume v, Kuhn length b, and crossover concentrations c*, c th, and c** into a semidilute polymer solution, a solution of overlapping thermal blobs and a concentrated polymer solution, respectively. This information is summarized as a diagram of states of different polysaccharide solution regimes by implementing a v/bl 2 and c/c** representation. The scaling approach is extended to the entangled solution regime, allowing us to obtain the chain packing number, P̃ e. This completes the set of parameters {B̂ g, B̂ th, P̃ e} which uniquely describes the static and dynamic properties of a polysaccharide solution.

Glyceraldehyde as an Efficient Chemical Crosslinker Agent for the Formation of Chitosan Hydrogels.

The rheological changes that occur during the chemical gelation of semidilute solutions of chitosan in the presence of the low-toxicity agent glyceraldehyde (GCA) are presented and discussed in detail. The entanglement concentration for chitosan solutions was found to be approximately 0.2 wt.% and the rheological experiments were carried out on 1 wt.% chitosan solutions with various amounts of GCA at different temperatures (25 °C and 40 °C) and pH values (4.8 and 5.8). High crosslinker concentration, as well as elevated temperature and pH close to the pKa value (pH ≈ 6.3–7) of chitosan are three parameters that all accelerate the gelation process. These conditions also promote a faster solid-like response of the gel-network in the post-gel region after long curing times. The mesh size of the gel-network after a very long (18 h) curing time was found to contract with increasing level of crosslinker addition and elevated temperature. The gelation of chitosan in the presence of other chemical crosslinker agents (glutaraldehyde and genipin) is discussed and a comparison with GCA is made. Small angle neutron scattering (SANS) results reveal structural changes between chitosan solutions, incipient gels, and mature gels.

Colloid-like solution behavior of computationally designed coiled coil bundlemers

The use of isotropic potential models of simple colloids for describing complex protein–protein interactions is a topic of ongoing debate in the biophysical community. This contention stems from the unavailability of synthetic protein-like model particles that are amenable to systematic experimental characterization. In this article, we test the utility of colloidal theory to capture the solution structure, interactions and dynamics of novel globular protein-mimicking, computationally designed peptide assemblies called bundlemers that are programmable model systems at the intersection of colloids and proteins. Small-angle neutron scattering (SANS) measurements of semi-dilute bundlemer solutions in low and high ionic strength solution indicate that bundlemers interact locally via repulsive interactions that can be described by a screened repulsive potential. We also present neutron spin echo (NSE) spectroscopy results that show high-Q freely-diffusive dynamics of bundlemers. Importantly, formation of clusters due to short-range attractive, inter-bundlemer interactions is observed in SANS even at dilute bundlemer concentrations, which is indicative of the complexity of the bundlemer charged surface. The similarities and differences between bundlemers and simple colloidal as well as complex protein–protein interactions is discussed in detail.

Extensional flow of stiff‐chain polymer solutions in the semidilute regime

AbstractStiff‐chain polymers are preponderant in biology as structural components of tissue and living cells. Hence, understanding their solution behavior under different flow histories is fundamental. Here, the extensional flow under capillary breakup of isotropic semidilute solutions of stiff‐chain poly‐n‐butyl isocyanate (PBIC) and hydroxypropyl cellulose (HPC) has been studied. PBIC‐chloroform and HPC‐water were studied as the polymer‐solvent interaction tunes the molecular conformation (Romo‐Uribe, J. Appl. Polym. Sci. 2021, 138, e49712). PBIC in chloroform exhibits a rod‐like conformation, and capillary breakup at constant concentration and temperature initially showed an exponential decay of filament diameter D(t) followed by a sudden decrease of D, and finally slow filament thinning. Increasing the molecular weight by threefold increased the breakup time τb by twofold. HPC in water adopts a semiflexible conformation and the filament thinning also exhibited three stages, however the breakup time was shorter than PBIC. Hence, the extensional viscosity as a function of strain of PBIC and HPC solutions exhibited three regimes, where initial constant extensional viscosity ηE was followed by strain hardening and finally a sudden decrease of extensional viscosity as strain increased. It was found that the filament breakup time τb is a function of the radius of gyration Rg.

Solution properties of N-(2-allyl-butyl ether)-O-carboxymethyl chitosan and N-(2-allyl-isooctyl ether)-O-carboxymethyl chitosan

pH-sensitive and amphiphilic chitosan derivatives can be used as hydrophobic drug carriers, and their rheological properties play a key role in their performance. In this paper, two pH-responsive and amphiphilic chitosan derivatives, N-(2-allyl-butyl glycidyl ether)-O-carboxymethyl chitosan (HBCC) and N-(2-ethylhexyl glycidyl ether)-O-carboxymethyl chitosan (H2ECC) were synthesized, and their rheological properties were studied. The influence of parameters including concentrations of HBCC and H2ECC, the degree of substitution, solution pH, and [Ca2+] on the rheological properties were investigated. The results showed that the overlap and entanglement concentration of HBCC and H2ECC was ca. 1.7 wt% and 5 wt%, respectively. The dilute and semidilute solutions showed Newtonian behavior. Above 5 wt%, strong networks formed, and shear-thinning behavior appeared at high shear rates (>10 s−1) for entangled solutions. A high degree of substitution and pH near the isoelectric points of HBCC and H2ECC corresponded to a low viscosity and viscoelasticity. In addition, Ca2+ played a shielding effect on the –COO− groups at low concentrations (<10 mmol/L), whereas it acted as a cross-linker when [Ca2+] ≥ 20 mmol/L. The intermolecular hydrogen bonds were examined by molecular dynamics simulations. The results provide new information related to the application of HBCC and H2ECC for hydrophobic drug packaging and transportation.

Diffusion and Viscosity of Unentangled Polyelectrolytes

We report chain self-diffusion and viscosity data for sodium polystyrene sulfonate (NaPSS) in semidilute salt-free aqueous solutions measured by pulsed-field gradient NMR and rotational rheometry, respectively. The molecular weight of NaPSS is characterized using five techniques. Relationships between Mw and the intrinsic viscosity and diffusion coefficient in excess salt are established. These are helpful for the accurate determination of the molar mass of NaPSS. The observed concentration dependence of η and D are consistent with the Rouse–Zimm scaling model if the monomeric friction coefficient (ζ) is concentration-dependent. The concentration dependence of ζ exceeds that expected from free-volume models of diffusion, and its origin remains unclear, possibly being related to electrostatic effects. Correlation blobs and dilute chains with equivalent end-to-end distances exhibit nearly equal friction coefficients, in agreement with scaling. Viscosity and diffusion data are combined using the Rouse model to calculate the single-chain dimensions of NaPSS in salt-free solution, and the results overpredict direct SANS measurements of the radii of gyration by a factor of ≃1.4.

Protamine-Controlled Reversible DNA Packaging: A Molecular Glue.

Packaging paternal genome into tiny sperm nuclei during spermatogenesis requires 106-fold compaction of DNA, corresponding to a 10-20 times higher compaction than in somatic cells. While such a high level of compaction involves protamine, a small arginine-rich basic protein, the precise mechanism at play is still unclear. Effective pair potential calculations and large-scale molecular dynamics simulations using a simple idealized model incorporating solely electrostatic and steric interactions clearly demonstrate a reversible control on DNA condensates formation by varying the protamine-to-DNA ratio. Microscopic states and condensate structures occurring in semidilute solutions of short DNA fragments are in good agreement with experimental phase diagram and cryoTEM observations. The reversible microscopic mechanisms induced by protamination modulation should provide valuable information to improve a mechanistic understanding of early and intermediate stages of spermatogenesis where an interplay between condensation and liquid-liquid phase separation triggered by protamine expression and post-translational regulation might occur. Moreover, recent vaccines to prevent virus infections and cancers using protamine as a packaging and depackaging agent might be fine-tuned for improved efficiency using a protamination control.

Effect of surface properties and polymer chain length on polymer adsorption in solution.

In polymer nanoparticle composites (PNCs) with attractive interactions between nanoparticles (NPs) and polymers, a bound layer of the polymer forms on the NP surface, with significant effects on the macroscopic properties of the PNCs. The adsorption and wetting behaviors of polymer solutions in the presence of a solid surface are critical to the fabrication process of PNCs. In this study, we use both classical density functional theory (cDFT) and molecular dynamics (MD) simulations to study dilute and semi-dilute solutions of short polymer chains near a solid surface. Using cDFT, we calculate the equilibrium properties of polymer solutions near a flat surface while varying the solvent quality, surface-fluid interactions, and the polymer chain lengths to investigate their effects on the polymer adsorption and wetting transitions. Using MD simulations, we simulate polymer solutions near solid surfaces with three different curvatures (a flat surface and NPs with two radii) to study the static conformation of the polymer bound layer near the surface and the dynamic chain adsorption process. We find that the bulk polymer concentration at which the wetting transition in the poor solvent system occurs is not affected by the difference in surface-fluid interactions; however, a threshold value of surface-fluid interaction is needed to observe the wetting transition. We also find that with good solvent, increasing the chain length or the difference in the surface-polymer interaction relative to the surface-solvent interaction increases the surface coverage of polymer segments and independent chains for all surface curvatures. Finally, we demonstrate that the polymer segmental adsorption times are heavily influenced only by the surface-fluid interactions, although polymers desorb more quickly from highly curved surfaces.

Interconnecting solvent quality, transcription, and chromosome folding in Escherichia coli

All cells fold their genomes, including bacterial cells, where the chromosome is compacted into a domain-organized meshwork called the nucleoid. How compaction and domain organization arise is not fully understood. Here, we describe a method to estimate the average mesh size of the nucleoid in Escherichia coli. Using nucleoid mesh size and DNA concentration estimates, we find that the cytoplasm behaves as a poor solvent for the chromosome when the cell is considered as a simple semidilute polymer solution. Monte Carlo simulations suggest that a poor solvent leads to chromosome compaction and DNA density heterogeneity (i.e., domain formation) at physiological DNA concentration. Fluorescence microscopy reveals that the heterogeneous DNA density negatively correlates with ribosome density within the nucleoid, consistent with cryoelectron tomography data. Drug experiments, together with past observations, suggest the hypothesis that RNAs contribute to the poor solvent effects, connecting chromosome compaction and domain formation to transcription and intracellular organization.

Dynamics and rheology of ring-linear blend semidilute solutions in extensional flow. Part I: Modeling and molecular simulations

We use Brownian dynamics (BD) simulations and single molecule experiments to investigate the influence of topological constraints and hydrodynamic interactions on the dynamics and rheology of solutions of ring-linear polymer blends at the overlap concentration. We find agreement between simulation and experiment in which rings in solution blends exhibit large conformational fluctuations. A subpopulation of rings shows extension overshoots in the startup of the flow, and other populations display tumbling and tank-treading at the steady state. Ring polymer fluctuations increase with the blend fraction of linear polymers and are peaked at a ring Weissenberg number WiR≈1.5. On the contrary, linear and ring polymers in pure solutions show a peak in fluctuations at the critical coil-stretch Weissenberg number Wi=0.5. BD simulations show that extension overshoots on the startup of the flow are due to flow-induced intermolecular ring-linear polymer hooks, whereas fluctuations at the steady state are dominated by intermolecular hydrodynamic interactions (HIs). This is supported by simulations of bidisperse linear polymer solution blends, which show similar trends in conformational dynamics between rings and linear polymers with a matched contour length. Compared to BD simulations, single molecule experiments show quantitatively larger fluctuations, which could arise because experiments are performed on higher molecular weight polymers with stronger topological constraints. To this end, we have advanced the understanding of the effects of topological interactions and intermolecular HIs on the dynamics of semidilute ring-linear polymer blend solutions.

Dynamics and rheology of ring-linear blend semidilute solutions in extensional flow: Single molecule experiments

Ring polymers exhibit unique flow properties due to their closed chain topology. Despite recent progress, we have not yet achieved a full understanding of the nonequilibrium flow behavior of rings in nondilute solutions where intermolecular interactions greatly influence chain dynamics. In this work, we directly observe the dynamics of DNA rings in semidilute ring-linear polymer blends using single molecule techniques. We systematically investigate ring polymer relaxation dynamics from high extension and transient and steady-state stretching dynamics in a planar extensional flow for a series of ring-linear blends with varying ring fraction. Our results show multiple molecular subpopulations for ring relaxation in ring-linear blends, as well as large conformational fluctuations for rings in a steady extensional flow, even long after the initial transient stretching process has subsided. We further quantify the magnitude and characteristic time scales of ring conformational fluctuations as a function of blend composition. Interestingly, we find that the magnitude of ring conformational fluctuations follows a nonmonotonic response with increasing ring fraction, first increasing at low ring fraction and then substantially decreasing at large ring fraction in ring-linear blends. A unique set of ring polymer conformations are observed during the transient stretching process, which highlights the prevalence of molecular individualism and supports the notion of complex intermolecular interactions in ring-linear polymer blends. In particular, our results suggest that transient intermolecular structures form in ring-linear blends due to a combination of direct forces due to linear chains threading through open rings and indirect forces due to hydrodynamic interactions; these combined effects lead to large conformational fluctuations of rings over distributed time scales. Taken together, our results provide a new molecular understanding of ring polymer dynamics in ring-linear blends in the nonequilibrium flow.

Nanoparticle dynamics in semidilute polymer solutions: Rings versus linear chains

We study the dynamics of nanoparticles in semidilute solutions of ring and linear polymers using hybrid molecular dynamics–multiparticle collision dynamics simulations. The dynamics of the monomers, the polymer centers-of-mass, and the nanoparticles coincide for these two architectures for solutions of the same monomer concentration. The long time diffusivities of the nanoparticles follow the predictions of a polymer coupling theory [Cai et al., Macromolecules 44, 7853–7863 (2011)], suggesting that nanoparticle dynamics are coupled to segmental relaxations for both polymer architectures examined here. At intermediate time scales, the nanoparticle dynamics are characterized by subdiffusive exponents, which markedly deviate from coupling theory and closely follow those of the polymers. Instead, the nanoparticle dynamics are strongly coupled to the polymer center-of-mass motions for both architectures, rather than to their segmental dynamics. The presence of ring concatenations does not affect the long-time diffusivity of the nanoparticles but leads to a slight decrease in the subdiffusive exponents of the nanoparticles and the polymer center-of-mass.

Dripping and jetting of semi-dilute polymer solutions co-flowing in co-axial capillaries

This work is focused on the mechanisms of the dripping and jetting flow modes of viscoelastic semi-dilute polyacrylamide aqueous solutions co-flowing with silicone oil in co-axial capillaries. A phase diagram of the dripping, jetting, and intermediate flow modes is established. It was found that in the dripping mode, the elongation velocity of the filament between the terminal droplet and the inner capillary is controlled solely by the continuous phase rate. At the same time, the decrease in the filament diameter is due to both stretching and outflow of the polymer solution into the terminal droplet. In the jetting mode, the thread diameter was found to evolve in three stages. In the first stage, the average jet velocity increases, whereas in the second and third stages, it becomes constant and corresponds to the velocity of the continuous phase. The transition from the second to the third stage is defined by the appearance of capillary waves resulting in the formation of the beads-on-string structure. In the third stage, the filament diameter between the neighbor beads decreases exponentially and is governed by the relaxation time, which strongly depends on polymer concentration, but does not depend on the continuous phase flow rate. A simple physical model was proposed for describing the evolution of dimensions of filaments and beads during development of jet capillary instability. The universal character of the evolution of filaments and beads sizes, which is independent of concentration of semi-diluted polymer solutions and flow rates of the continuous phase, is revealed.

Abstract P-38: Tunable Soft Networks of Wormlike Micelles and Clay Particles

Background: Over the past few decades, there has been a great deal of interest in the aqueous self-assembly of surfactant molecules into giant wormlike micelles (WLMs). These cylindrical aggregates undergo reversible breakdown processes and in favorable cases can grow up to few tens of micrometers that is comparable with the length of high molecular weight polymer. The viscoelastic properties of WLMs can be easily modified by different additives like salts or polymers. A new emerging research area consists of tuning the WLM solution properties by inorganic nanoparticles. It suggests, in particular, the use of networks of entangled WLMs as a matrix for producing soft nanocomposites with different kinds of embedded nanoparticles that are promising for controlled release, template synthesis, and oilfield applications. These materials can combine adaptive rheological properties of the WLM matrix and the functionality of nanofiller. Methods: Rheometry and cryo-transmission electron microscopy were combined to investigate the structure and properties of mixed WLMs of zwitterionic oleylamidopropyl dimethyl betaine and anionic sodium dodecyl sulfate surfactants and platelike particles of bentonite clay. Results: This system demonstrates the formation of giant linear long-lived WLMs, which even at extremely low surfactant concentrations reach a sufficient length to entangle with each other and form a temporally persistent network. The stability of these micelles can be due to electrostatic attraction between the headgroups of the anionic and zwitterionic surfactants and favorable volume/length hydrophobic ratio in the surfactant mixture. At increasing surfactant concentration, the long-lived linear micelles transform into fast-breaking branched micelles. Stable viscoelastic suspensions of clay particles in semi-dilute solutions of WLM were elaborated. They represent a novel type of soft nanocomposite with the tunable matrix. Structural studies revealed that the clay is dispersed in a dense network of entangled WLM in the form of 100-nm tactoids. Rheological investigations demonstrated that clay particles can induce an increase of viscosity and relaxation time by up to one order of magnitude. The effect of the clay becomes more pronounced with increasing content of anionic surfactant, when the micelles become branched. This behavior was explained by the stabilization of micelle-nanoclay junction points due to the screening of the repulsion between positively charged fragments of zwitterionic head groups by added anionic surfactant. Conclusion: The pronounced effect of nanoparticles on the viscoelasticity of the network formed by branched WLMs was observed for the first time. The nanoparticles-WLM junctions were confirmed by cryo-TEM data. The elaborated systems are of interest for many industrial applications.

The Effects of Weak Viscoelasticity on Enhanced Particle Removal for CMP

Highly elastic solutions have been shown to increase particulate removal from silicon wafers, indicating the possibility for reduced reliance upon hazardous chemicals and expensive technologies during post-CMP cleaning processes. We explored the onset of this enhanced removal using micron-sized silica particles in rinsing and siphoning experiments with polymer fluids of high molecular weights that ranged from dilute to entangled concentrations. Increases in particle removal with less than 100 ppm of polymer were observed using both methods, with 10% increased removal observed in the rinsing experiment and 4% increased removal in the siphoning experiment relative to water. Further increases in polymer concentration increased removal significantly, as the solutions entered the semidilute regime. Highly concentrated solutions showed “streaking” patterns, consistent with the viscoelastic nature of the solution. Additionally, we examined particle removal as a spatially dependent parameter in siphoning experiments, showing a plateau of significant removal near the siphon with a sharp decay to a constant value at distances farther away from the siphon.Rheological characterization of the siphoning and rinsing polymer solutions was used to explore relationships between observed removal and solution properties. Increases in particle removal with solutions having nearly indistinguishable shear rheology and immeasurable extensional character were observed, indicating the need for more precise methods for extensional characterization of dilute polymer solutions. The application of polymer solutions to particle-removal processes has the potential to simplify post-CMP cleaning and reduce the environmental impact that is associated with present particle-removal chemistries. Figure 1: Removal profile of micron-sized silica particles on glass slides that were subjected to fluid siphoning. Crosshairs indicate the point on the glass slide directly under siphon. Siphoning solutions consisted of water (a), and poly (ethylene oxide) at concentrations of 50, 100, 500, 1000, and 5000 parts-per-million (b-f, respectively). Particulate area was determined by the total pixel count of silica particles in each image. Removal profiles for dilute solutions (a-c) show similar spatial dependence with mild increases in average removal. Removal profiles for semidilute solutions (d-e) show clear radial dependence while the concentrated solution showed behavior associated with significant elastic character. Figure 1

Electrostatics, conformation, and rheology of unentangled semidilute polyelectrolyte solutions

Polyelectrolyte (PE) solutions, which are charged polymers in polar solvents, are ubiquitous and essential to life. Due to the electrostatic interactions among the charged monomers and mobile ions, the dependence of the rheological properties on the polymer concentration of PE solutions differs significantly from that of solutions of uncharged macromolecules. In addition, salt in PE solutions, whether added intentionally or intrinsically present, can affect the properties of the solutions. Here, we analyze the ion distribution near a monomer using the nonlinear Poisson–Boltzmann equation for scenarios with nonoverlapping and overlapping electric double layers. Consequently, by incorporating the electrostatic interactions into the blob model and Zimm–Rouse dynamic model, we obtain different scaling laws for the electrostatic energy per monomer, correlation length, end-to-end distance, relaxation time and viscosity η of semidilute, unentangled PE solutions in consecutive regimes of polymer concentration np, and salt concentration ns, which are summarized in tables. With our theory, we anticipate that the empirical Fuoss law η∝np1/2 is expected for solutions prepared with salt-contaminated PE samples, while η∝np0.68 might be found for those with purer PE samples. A new critical charge fraction φc is defined, where we predict that the peak, which is present in the measurements of the reduced viscosity η/np as a function of np, is only expected for weakly charged PEs φ&amp;lt;φc prepared with pure PE samples. Comparisons with the experimental data as well as the classical scaling theories are provided, and the range of applicability of the theory is discussed.

Slip and Friction Mechanisms at Polymer Semi-Dilute Solutions/Solid Interfaces

The role of the polymer volume fraction, $\phi$, on steady state slippage and interfacial friction is investigated for a semi-dilute polystyrene solutions in diethyl phthalate in contact with two solid surfaces. Signicant slippage is evidenced for all samples, with slip lengths b obeying a power law dependence. The Navier's interfacial friction coecient, k, is deduced from the slip length measurements and from independent measurements of the solutions viscosity $\eta$. The observed scaling of k versus $\phi$ clearly excludes a molecular mechanism of friction based on the existence of a depletion layer. Instead, we show that the data of $\eta$($\phi$) and k($\phi$) are understood when taking into account the dependence of the solvent friction on $\phi$. Two models, based on the friction of blobs or of monomers on the solid surface, well describe our data. Both points out that the Navier's interfacial friction is a semi-local phenomenon.

Characterization of hydrophobic interaction of galactomannan in aqueous solutions using fluorescence-based technique

Fluorescence probing was used to study hydrophobic interactions of galactomannan (GM) obtained from fenugreek gum (FG), guar gum (GG), and locust bean gum (LBG) at different M/G ratios. The I1/I3 ratio of pyrene changed from 1.73 to 1.29, 1.22, and 1.29 for FG, GG and LBG, respectively, as the concentration of GM increased from 0.01 to 8.0 g/L at 30 °C. The critical aggregation concentration of FG, GG, and LBG increased from 1.04 to 3.84 g/L, 1.15 to 3.73 g/L, and 0.94 to 3.63 g/L, respectively, as temperature increased from 10 to 70 °C. Addition of Na2SO4 and NaSCN increased the I1/I3 ratio in dilute solution, but reduced it in semi-dilute solution, whereas adding urea reduced I1/I3 in dilute solution but increased it in semi-dilute solution. These results indicated that the CAC of GM, polarity and number of hydrophobic microdomains were highly dependent on the M/G ratio and galactose distribution.

Dynamics of Flexible Viruses in Polymer Solutions

We examine the coupling of the dynamics of flexible viral nanoparticles to the dynamics of comparably sized polymer chains. Using fluorescence microscopy, we quantify the dynamics of three filamentous viruses, potato virus M (PVM), M13, and pf1, that are suspended in semidilute solutions of partially hydrolyzed polyacrylamide. The dynamics of the viral nanoparticles are approximately diffusive on accessible time and length scales, but the distributions of displacements are non-Gaussian and exhibit increasingly extended tails as the aspect ratio of the viruses or the polymer concentration is increased. The long-time diffusion coefficients do not collapse onto a universal curve based on existing models for rodlike or spherical nanoparticles that are comparably sized to the polymer chains. Instead, the diffusivities appear to collapse as a function of the ratio of the polymer correlation length and a length scale intermediate between the virus radius and length, indicating that the hydrodynamic coupling to the polymer dynamics is affected by the virus anisotropy and flexibility.