Polymer Hydrodynamic Radius Research Articles

Diffusion Coefficients of Coated Plasmonic Nanoparticles in Viscous Environment.

The Stokes-Einstein relationship (SER) is not valid anymore in polymeric solutions for nanoparticles. It is thus important to characterize theirdiffusion properties to get a finer understanding of their behavior and to better tune their attributes for biomedical applications. The diffusion of gold and silver nanoparticles with citrate, hyaluronic acid, methyl-polyethylene glycol, and antibody-polyethylene glycol coatings is studied in hyaluronic-based viscous solutions. The diffusion coefficient D is estimated from the Brownian motion thanks to a cost-effective side-illumination device. It is determined that the nanoparticles (hydrodynamic radius rh: 30-135nm) diffuse up to 4-5 times faster than expected using the SER with a macroscopic viscosity from 1 to 30 mPa·s. It is shown that the adapted Huggins equation is a good model to describe the diffusion behavior of nanoparticles using an effective viscosity ηeff given by where where E is the polymer correlation length, Rh the polymer hydrodynamic radius and ηs the solvent viscosity. The values of k and a are given and allow to obtain D with an error of 10-20%. The impact of chemical interactions on the model parameter values are also highlighted, especially due to electrostatic interactions between the polymer and the nanoparticles.

Tailoring polycarboxylate architecture to improve the rheological properties of cement paste

This study elucidates the link between polycarboxylate (PC) architecture (random vs. block) and rheological properties of cement pastes at a low water-cement ratio (W/C = 0.22) through a systematic investigation on the rheological properties, adsorption properties, solution viscosity and polymer hydrodynamic radius. Adsorption data show that the adsorption amount of the block PC is larger than that of the random PC while the paste flow is the same even though the dosage of the former is smaller, possibly owing to the fact that the adsorbing carboxylic groups are concentrated at one end in the case of the block PC, and the absence of neutral side chains in the adsorbing block effectively reduces the free energy barrier of PC adsorption. Results on the polymer hydrodynamic radius from dynamic light scattering (DLS) illustrate that the hydrodynamic radius of the block PC is smaller than that of the random PC, and in consistence with the DLS results, the solution of the block PC is also found to have a lower viscosity at the same polymer weight concentration. It is worth-noting that the apparent viscosity of the cement paste has a close relation with the viscosity of PC remaining in solution. The dual effects of a larger adsorption amount and a smaller hydrodynamic radius of the block PC effectively reduce the viscosity of PC remaining in solution, and hence effective reduce the apparent viscosity of cement pastes. It is believed that this study allows for a better understanding of the influences of polycarboxylate architecture on rheological properties of cementitious materials.

Size-exclusion and the void volume of HPLC column

Size-exclusion chromatography (SEC) is the main technique for determination of polymer molecular weight distribution. SEC elution volumes are limited by column void volume and interparticle volume. Measurements of these volumes at actual size-exclusion conditions is discussed together with the relationship of polymer retention to its hydrodynamic volume. We studied the retention of 32 polystyrene standards with polydispersity below 1.05 on 10 different commercial columns. Nine columns had silica based C18 modified packings, and one, polymer-based packing. Pore sizes of packing materials varied from 8 to 35 nm, and 3 packings were poroshell type. Propagation of the retention dependence on the cubic root of the polymer molecular weight to zero mass value was shown to correspond to the column void volume; and was consistent with other methods of void volume measurement. Observed linear dependencies of retention volumes on for low molecular weight polymers on all studied columns suggests a correlation between the product of the polymer hydrodynamic radius and the adsorbent surface area. This correlation is thoroughly discussed.

ASP flooding in tight carbonate rocks

Alkaline-Surfactant-Polymer (ASP) floods can mobilize oil left behind by waterfloods by lowering the interfacial tension. However, conducting such floods in tight carbonate rocks presents several challenges, e.g., polymer transport in low permeability carbonates, presence of divalent ions, geochemical interactions with chemicals and rock surface, pore-scale heterogeneity, and oil-/mixed-wettability. This paper addresses the first three challenges. A systematic study of polymer transport in low permeability carbonate cores was performed. Shearing of high molecular weight polymers and successive filtration treatment were performed to improve polymer size distribution. Single phase polymer transport experiments were performed in low permeability carbonate rocks, and optimum pretreatment method was developed. Surfactant phase behavior and aqueous stability experiments were performed to develop ultralow tension ASP and SP formulations with a reservoir crude oil. ASP and SP corefloods were performed in oil-wet low permeability limestone rocks. The oil recovery, pressure drop, effluent ionic composition, effluent viscosity and effluent surfactant concentrations were measured. PHREEQC simulations were performed to understand geochemical reactions during ASP floods. The polymer treatment procedure was able to successfully transport polymer through low permeability Edwards Yellow limestone cores, but not through Texas Cream limestone due to differences in their pore structures. It was found that polymer hydrodynamic radius must be smaller than the pore throat radii of the rock for successful polymer transport. Therefore, mercury porosimetry data of the porous medium is critical for polymer selection, especially in case of low permeability rocks. Tertiary ASP floods resulted in improving the cumulative oil recovery to 77–87% OOIP, whereas SP flood improved the cumulative oil recovery to 85% in an outcrop core. Surfactant retentions during ASP and SP corefloods were found to be 0.4 mg/g-rock and 0.3 mg/g-rock, respectively, in outcrop cores.

Polymers in 2D confinement: A nanoscale mechanism for thermo‐mechanical reinforcement

Acrylate‐clay nanocomposites, a 2D confined system, exhibited unusual increase of thermo‐mechanical properties. The nature of this reinforcement can be ascribed to chain dynamics modification and therefore investigated via dynamic mechanical analysis. Transmission electron microscopy and dynamic light scattering showed a strong nanoconfined regime, 2Rh ≫ d001, whereRhis the polymer's hydrodynamic radius andd001is the clay gallery spacing. The geometrical constraints to polymer dynamics led to significantenhancementof the thermo‐mechanical properties. Adding only 1 wt% nanoclay, the glass transition temperature increased significantly,ΔTg = Tg − Tg,bulk ~ 10°C, and the dynamic modulusE′ increased 10‐fold. Analysis of dynamic mechanical spectra showed an increase of relaxation timeτ, ie, polymer dynamics retardation. Furthermore, the mechanical damping tanδwas strongly attenuated evidencing the reduction of viscous dissipation. The activation energyEaof theα‐transition increased as the confined macromolecules needed to overcome higher energy barriers to achieve configurational rearrangements. The considerable increase of mechanical modulus cannot be explained by polymer composite models, rather it was associated to a “nano‐effect,” scaling with the degree of confinement asE/Ematrix ~ (2Rh/d001)n. This study paves the road for further understanding of polymer dynamics under 2D confinement and the reinforcement mechanism of thermo‐mechanical properties.

Quantifying chloride binding and salt extraction with poly(methyl methacrylate) copolymers bearing aryl-triazoles as anion receptor side chains.

Copolymers of methyl methacrylate and aryl-triazole based anion receptors were quantitatively analyzed. Transfer of structural features (1 : 1 and 2 : 1 complexes) and Cl(-) affinities from the parent receptors was demonstrated. Cl(-)-induced cross-linking changed the polymer's hydrodynamic radius. Extraction of tetrapropylammonium Cl(-) from water to dichloromethane was enhanced over PMMA.

Activation Energy for Mobility of Dyes and Proteins in Polymer Solutions: From Diffusion of Single Particles to Macroscale Flow

We measure the activation energy Ea for the diffusion of molecular probes (dyes and proteins of radii from 0.52 to 6.9 nm) and for macroscopic flow in a model complex liquid-aqueous solutions of polyethylene glycol. We cover a broad range of polymer molecular weights, concentrations, and temperatures. Fluorescence correlation spectroscopy and rheometry experiments reveal a relationship between the excess of the activation energy in polymer solutions over the one in pure solvent ΔEa and simple parameters describing the structure of the system: probe radius, polymer hydrodynamic radius, and correlation length. ΔEa varies by more than an order of magnitude in the investigated systems (in the range of ca. 1-15 kJ/mol) and for probes significantly larger than the polymer hydrodynamic radius approaches the value measured for macroscopic flow. We develop an explicit formula describing the smooth transition of ΔEa from the diffusion of molecular probes to macroscopic flow. This formula is a reference for the quantitative analysis of specific interactions of moving nano-objects with their environment as well as active transport. For instance, the power developed by a molecular motor moving at constant velocity u is proportional to u2exp(Ea/RT).

Suction of hydrosoluble polymers into nanopores

Forced penetration of large hydrosoluble polymer chains through track-etched membranes has been investigated as a function of both solvent flow rate in the pores and the ratio of polymer hydrodynamic radius to pore radius. We measure the rejection coefficient Robs from retentate and permeate mean concentrations, and its corrected value R including polymer accumulation at the membrane. The variations of R as a function of solvent flow rate per pore in adimensional units collapse into the same curve well fitted by de Gennes' “suction model”. This curve, universal for flexible polymers in good solvents, leads to an estimate of the critical penetration flow.

Preparation and Solution Behavior of a Thermoresponsive Diblock Copolymer of Poly(ethyl glycidyl ether) and Poly(ethylene oxide)

A thermoresponsive diblock copolymer, poly(ethyl glycidyl ether)-block-poly(ethylene oxide) (PEGE-b-PEO), is synthesized by successive anionic ring-opening polymerization of ethyl glycidyl ether and ethylene oxide using 2-phenoxyethanol as a starting material, and its solution behavior is elucidated in water. In a dilute 1 wt % solution, the temperature-dependent alteration in the polymer hydrodynamic radius (RH) is measured in the temperature range between 5 and 45 degrees C by pulse-gradient spin-echo NMR and dynamic light scattering. The RH value increased with temperature in two steps, where the first step at 15 degrees C corresponds to the core-shell micelle formation and the second step at 40 degrees C corresponds to the aggregation of the core-shell micelles. The formation of the core-shell micelles is supported by the solubilization of a dye (1,6-diphenyl-1,3,5-hexatriene) in the hydrophobic core, which is recognized for a copolymer solution in the temperature range between 20 and 40 degrees C. In this temperature range, the core-shell micelles and the unimers coexist and the fraction of the former gradually increases with increasing temperature, suggesting equilibrium between the micelles and the unimers. In the concentrated regime (40 wt % solution), the solution forms a gel and the small-angle X-ray scattering measurements reveal the successive formation of hexagonal and lamellar liquid crystal phases with increasing temperature.

Effect of Pore Size on Adsorption of a Polyelectrolyte to Porous Glass

The adsorption of quaternized poly(vinylpyridine) (QPVP) on controlled pore glass (CPG) size, over the ionic strength range 0.001-0.5 M was found to display nonmonotonic behavior as a function of pore size. Both adsorption kinetics and ionic strength effects deviated dramatically from behavior typical of adsorption on flat surfaces when the ratio of the pore radius Rp to the polymer hydrodynamic radius Rh became smaller than ca. 2. Ionic strength enhancement of adsorption for small pore sizes was observed at much higher salt concentrations than is typical for polycation adsorption on flat surfaces. The amount of polymer adsorbed per unit surface area of glass GammaA, in 0.5 M NaCl, exhibited a shallow maximum at Rp/Rh approximately 5. Since the value of GammaA for small pore size CPG is strongly depressed by the large surface area, an alternative and more interesting observation is that the amount of polymer adsorbed per gram of CPG, Gammaw, displays a strong maximum when Rp is equal to or slightly smaller than Rh. The efficiency with which QPVP binds anionic micelles to (negatively charged) CPG (grams of surfactant/grams of QPVP) increases strongly with diminishing pore size, indicating that the configuration of polycation bound to small pores favors micelle binding. Since the micelles are larger than small pores, the results indicate that when Rp < Rh, adsorbed polycation molecules reside only partially within the pore. The results of this study are supported by simulations of polyelectrolytes within cylindrical cavities.

Relaxational mode structure for optical probe diffusion in high molecular weight hydroxypropylcellulose

We studied translational diffusion of dilute monodisperse spheres (diameters 14 < d < 455 nm) in aqueous 1 MDa hydroxypropylcellulose (0 ≤ c ≤ 7 g/L) at 25°C using quasielastic light scattering. Spectra are highly bimodal. The two spectral modes (“slow,” “fast”) have different physical properties. Probe behavior differs between small (d < Rh) and large (d ≥ Rg) probes; Rh and Rg are the matrix polymer hydrodynamic radius and the radius of gyration, respectively. We examined the dependences of spectral lineshape parameters on d, c, scattering vector q, and viscosity η for all four probe-size and mode-type combinations. We find three time scale-separated modes: (1) a large-probe slow mode has properties characteristic of particle motion in a viscous medium; (2) a large-probe fast mode and small-probe slow modes share the same time scale, and have properties characteristic of probe motion coupled to internal chain dynamics; and (3) a small-probe fast mode has properties that can be attributed to the probe sampling local chain relaxations. In the analysis, we also attempted to apply the coupling/scaling (CS) model of Ngai and Phillies [Ngai, K. L., Phillies, G. D. J. J. Chem. Phys., 105, 8385 (1996)] to analyze our data. We find that the second mode is described by the coupling/scaling model for probe diffusion; the first and third modes do not follow the predictions of this model. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3087–3100, 1998

Corrections to preaveraging approximation within the Kirkwood–Riseman model for flexible polymers: Calculations to second order in ε with both hydrodynamic and excluded volume interactions

The polymer hydrodynamic radius RH is calculated to second order in the ε=4−d (d is the dimension) perturbation theory using the Kirkwood–Riseman model in conjunction with the renormalization group. Excluded volume effects on RH are modeled by the two-parameter theory, and the hydrodynamic radius is evaluated both with and without the preaveraging approximation. These second order in ε calculations are then used to evaluate the leading corrections in ε to the preaveraging approximation for RH. Gaussian and self-avoiding chains in three dimensions yield nondraining limit preaveraging corrections of 26% and 16%, respectively, whereas simulations by Zimm and others using the same rigid body model of dynamics produce only about a 12% correction for Gaussian chains. It thus appears that the dynamical renormalization group theory only provides a qualitative prediction of the preaveraging error to this order in the ε-perturbation theory.

Gel permeation chromatography with crosslinked polystyrene gels and poor and theta solvents for polystyrene, 2. Separation mechanism

AbstractFor separations performed with crosslinked polystyrene gels, an interpretation is proposed for the displacement to high retention volume of plots of log hydrodynamic volume versus retention volume for polystyrene (PS) in poor and theta solvents, e.g. cyclohexane, trans‐decalin, and N,N‐dimethylformamide, with respect to plots for other polymers for which these same eluents are good solvents. PS separates by steric exclusion and by solute‐gel interaction effects giving rise to partition and adsorption mechanisms. The retention volume VR is given by where V0 is the interstitial volume, Vi is the solvent volume within the gel, KD is the distribution coefficient for steric exclusion, and Kp is the distribution coefficient for solute‐gel interaction effects. For polymers in good solvent media separating solely by steric exclusion, Kp is unity. For PS in poor and theta solvents, network‐limited partition and network‐limited adsorption mechanisms are proposed in which Kp is greater than unity. The hydrodynamic volume universal calibration method is applicable when Kp is greater than unity, provided the retention parameter is changed from VR to (VR–V0)/Kp. From the network‐limited adsorption mechanism, a plot of log[(VR–V0)/Kp] versus polymer hydrodynamic radius yields the average pore size of the crosslinked polystyrene gel. Experiments are reported showing the dependence of Kp on gel porosity and on solvent power by varying the temperature of the eluent.