Dilute Solution Regime Research Articles

Mechanistic Understanding of Long Duration Fast Charge Aqueous Zinc Batteries Using Physically Adsorbed Oligomers as Interphases.

Polymers have been used as additives in the liquid electrolytes typically used for secondary batteries that utilize metals as anode. Such additives are conventionally argued to improve long-term anode performance by suppressing morphological and hydrodynamic instabilities thought to be responsible for out-of-plane and dendritic metal deposition during battery charging. More recent studies have reported that the polymer additives provide even more fundamental mechanisms for stabilizing metal electrodeposition through their ability to regulate metal electrodeposit crystallography and, thereby, morphology. Few studies explore how polymers carried in a liquid electrolyte achieve these functions, and fewer still provide rules for choosing among the various polymer types, the additive polymer molecular weight (Mw), and concentration in the electrolyte. Here, we investigate how these generally easy-to-control variables influence electrochemical interphase formation inside battery cells and their impact on the morphology and reversibility of Zn electrodes in aqueous electrolytes. We focus on aqueous Zn-iodine electrochemical cells containing linear polyethylene glycol (PEG) chains as additives and find that in electrolytes where the polymer concentration is maintained in the dilute solution regime there is an optimum polymer molecular weight (Mw ≈ 1000 Da), above which beneficial effects of polymers on Zn electrode reversibility and Zn-I2 battery lifetime are progressively lost. By means of optical ellipsometry and theoretical calculations, we show that the optimal Mw is associated with saturation of the thickness of a physiosorbed PEG coating on the Zn metal electrode. Electron microscopy and X-ray photoelectron spectroscopy analysis of Zn electrodeposits formed in such electrolytes reveal that the physiosorbed polymer coating has two primary effects─it regulates the deposit morphology and suppresses parasitic reactions between the electrode and electrolyte components. The parasitic reactions produce species like ZnO, which are known to passivate the Zn electrode and promote nonuniform deposition. Galvanostatic cycling measurements in aqueous Zn-I2 cells containing the PEG additives at the optimal Mw show that the cells maintain very high Coulombic efficiencies (≥99%) at current densities as high as 50 mA/cm2─close to the maximum values permissible across the Celgard separator membranes used in our studies.

Estimation of evaporation rate of cesium from hot sodium pool to inert cover gas of typical SFR

Estimation of evaporative release of Cesium-137 (Cs-137) from the hot pool of Sodium cooled Fast Reactor (SFR) under normal operating condition and hypothetical core meltdown accident scenario is important in safety analysis due to the radiological consequences associated with Cs release. A methodology has been developed to estimate the cesium evaporation rate from hot pool to inert cover gas region of typical SFR under fuel pin clad failure scenario based on the temperature and concentration dependent activity coefficient of cesium estimated using the Flory–Huggins solution theory. The predicted equilibrium partition coefficient (KD) values of cesium are validated with theoretical and experimental data available in literature. It has been observed that the KD of cesium is decreasing with increase in Cs concentration. A correlation has been developed for KD as a function of temperature in the infinite dilute solution regime. The present methodology predicted Retention Factor (RF) values of Cs based on the estimated KD values are closer to the experimental results compared to the published results of empirical models in the SFR hot pool temperature range. The methodology has been used for evaluating the evaporative release of cesium along with sodium from hot pool to cover gas region of typical SFR under fuel pin clad failure scenario. These estimations are useful for evaluating the radioactive dose due to Cs transport from SFR sodium pool to its inert argon cover gas region.

Asphaltene Aggregation and Solubility

An attenuated association model describing the aggregation of asphaltenes in solution is extended to derive an equation for the weight-average degree of association and account for phase behavior. The weight-average molecular weight is calculated to be higher than number average, as it must be for a polydisperse material, but not by enough to explain the very large differences in these quantities reported in the literature. Binodals and spinodals are calculated using expressions derived previously, but modified to account for free volume (thermal expansion) differences. The phase behavior of asphaltene solutions is examined in more detail, particularly in the dilute solution regime. It is shown that the formation of nanoaggregates significantly affects the critical value of the χ interaction parameter. The phase diagram is highly asymmetric and the phase boundary approaches the pure solvent composition limit. This has a number of implications in terms of asphaltene solution characterization and the nature...

Estimation of retention factor of cesium in sodium pool under fuel pin failure scenario in SFR

Abstract Radioactive source term in argon (Ar) cover gas region of the primary vessel due to cesium (Cs) leaked from the failed fuel pins into the primary coolant of Sodium cooled Fast Reactor (SFR) depends on its thermodynamic and kinetic behavior with the coolant sodium. Evaluation of this source term requires detailed knowledge on the distribution of Cs between large volume of the liquid sodium, and the inert Ar cover gas. Solute–solvent combination like liquid Cs and sodium, with relative volatility greater than unity, is an important system to be analyzed in the context of SFR safety. Distribution of Cs between Ar cover gas and liquid sodium pool is complicated by the imposition of temperature difference across the cover gas region and its resultant enrichment of the more volatile solute. An analytical model has been developed to obtain the geometry dependent Retention Factor (RF) of Cs in the sodium pool as a function of the height of cover gas, initial mass inventory of Cs, the temperature difference across the cover gas region (between the sodium pool surface and top roof bottom plate) for an infinite dilute solution of Cs in the sodium pool. The model predicted results are validated with available experimental results in the literature and found that they are fairly in good agreement. In the infinite dilute solution (IDS) regime sodium pool is having the retention capacity to keep the Cs from being released into the argon cover gas region.

Drop-on-demand drop formation of polyethylene oxide solutions

The dynamics of drop-on-demand (DOD) drop formation for solutions containing polyethylene oxide (PEO) have been studied experimentally. Using a piezoelectrical actuated inkjet printhead with the nozzle orifice diameter of 53 μm, experiments were conducted for a series of PEO aqueous solutions with molecular weights ranging from 14 to 1000 kg/mol, polydispersity from 1.02 to 2.5, and concentrations from 0.005 to 10 wt. %. The addition of a small amount of PEO can have a significant effect on the DOD drop formation process, increasing breakup time, decreasing primary drop speed, and decreasing the number of satellite drops in some cases. The effects depend on both molecular weight and concentration. At lower molecular weights (14 and 35 kg/mol), the effect of PEO over the dilute solution regime is insignificant even at concentrations large enough that the solution does not fall in the dilute regime. As PEO molecular weight increased, the effects became significant. For monodispersed PEO solutions, breakup time and primary drop speed closely correlated with effective relaxation time but not for polydispersed PEO. Effective relaxation time depended greatly on molecular weight distribution. Viscosity-average molecular weight, used in calculating effective relaxation time for polydispersed PEO solutions, did not adequately account for high molecular fractions in the molecular weight distribution of the polydispersed PEOs. A mixture rule was developed to calculate the effective relaxation times for aqueous solutions containing mixtures of monodispersed PEO, and breakup times and primary drop speeds correlated well with effective relaxation times. For our experiments, DOD drop formation was limited to Deborah number ≲ 23.

Molecular interaction in some polymeric additive solutions containing styrene-hydrogenated butadiene copolymer

The miscibility of styrene-hydrogenated butadiene copolymer (SHB) with different constituents of polymer additives for lubricating mineral oils was studied in dilute solution regime, using xylene as model solvent, at 30 °C, in a wide range of polymer blend compositions. The systems studied were SHB/poly(ethylene- co-propylene) (EPC), SHB/poly(methyl methacrylate) (PMMA), SHB/poly(dodecyl methacrylate) (PDDMA) and SHB/polystyrene (PS). The viscometric interaction parameters were calculated according to the Krigbaum–Wall and Catsiff–Hewett models of ideal viscometric behavior. Strong repulsive interactions were found in SHB/PMMA and SHB/PDDMA systems pointing to immiscibility. SHB/EPC and SHB/PS deviated much less from ideality. The results were compared to the theoretical estimation of interaction in polymer blends in the absence of solvent, using the Coleman–Graf–Painter approach. No correlation was observed between the interaction in the bulk and in solution.

Synthesis and Physicochemical and Dynamic Mechanical Properties of a Water-Soluble Chitosan Derivative as a Biomaterial

The physicochemical and rheological properties of a water-soluble chitosan (WSC) derivative were characterized in order to facilitate its use as a novel material for biomedical applications. The WSC was prepared by conjugating glycidyltrimethylammonium chloride (GTMAC) onto chitosan chains. Varying the molar ratio of GTMAC to chitosan from 3:1 to 6:1 produced WSCs with a degree of substitution (DS) that ranged from 56% to 74%. The WSC with the highest DS was soluble in water up to concentrations of 25 g/dL at room temperature. An increase in the polymer concentration gradually increased both the pH and conductivity of the WSC solutions. The rheological properties of the WSC solutions were found to be dependent on the salt and polymer concentrations as well as the DS value. In the absence of salt, the rheological behavior of the WSC was found to be typical of that for a polyelectrolyte in the dilute solution regime. However, the addition of salt decreased the viscosity of the polymer solution due to the reduction of electrostatic repulsions by the positively charged trimethylated ammonium groups of the WSC. In the concentrated regime, the viscosity of the WSCs was found to follow a power-law expression. The lowest DS WSC had the more favorable viscoelastic properties that were attributed to its high molecular weight, as confirmed by the stress relaxation spectra and intrinsic viscosity measurements. The effect of DS on the degree of interaction between WSC and the lipid egg phosphatidylcholine was investigated by FTIR analysis. Overall, the lower DS WSC had enhanced rheological properties and was capable of engaging in stronger intermolecular physical interactions.

Interaction between Silicates and Ionic Surfactants in Dilute Solution

Understanding the interaction between silicate ions and surfactants is critical for the design and development of mesoporous siliceous materials. We examined the interaction between sodium silicate ions and three different cationic surfactants [namely, cetyltrimethylammonium bromide (CTAB), tetradecyltrimethylammonium bromide (TTAB), and dodecyltrimethylammonium bromide (DTAB)] and an anionic surfactant [sodium dodecyl sulfate (SDS)] in dilute solution at room temperature. From the combination of several techniques, such as conductometric and potentiometric titrations, dynamic light scattering, and isothermal titration calorimetry, the phase behavior of the sodium silicate and CTAB system was determined. We observed that the aggregation behavior of the silicate-CTAB system is similar to that of a polymer-surfactant system. The formation of the silicate-CTAB complex is induced by the adsorption of SiOH and SiO- groups, aided by CTAB unimers. The electrostatic attraction and hydrophobic interaction are the dominant forces controlling the formation of silicate-CTAB complexes. When these complexes are saturated with CTAB unimers, free CTAB micelles are then produced. TEM micrographs revealed that a stable Si-O-Si network is absent within the silicate-CTAB complexes, and surprisingly, stable silicate-CTAB complexes with ordered structure were observed. The present finding is important for understanding the interaction between silicate and surfactant in the synthesis of mesoporous structure in the dilute solution regime.

Polymer Solution Model with Anisotropic Phase

We investigate a lattice self-avoiding walk model with directive (hydrogen bond like) interactions between chain segments and isotropic interactions between monomers and solvent molecules. The model, meant to describe a polymer in the dilute solution regime, is investigated in the framework of the Bethe approximation. Directive interactions produce, in addition to the ordinary collapse, a first order transition to an anisotropic (structured) phase. The interplay with solvent interactions modifies the nature of the isotropic phase, which can be either swollen or collapsed. Such an interplay may be an important ingredient for the formation of ordered structures in biopolymers. The relationship with previously investigated self-avoiding walk models is also discussed.

Oscillatory Packing and Depletion of Polyelectrolyte Molecules at an Oxide−Water Interface

Total internal reflection microscopy (TIRM) has been used to study the interactions between a 5 μm borosilicate glass sphere and a silica slide in the presence of a nonadsorbing polyelectrolyte, sodium (polystyrene sulfonate) (NaPSS). The effect of the polymer concentration, within the dilute solution regime, on the observed interactions was investigated. In all cases, the interactions displayed a short-range electrostatic repulsion followed immediately, at larger separations, by a decaying oscillatory interaction that is attributed to structuring of the polyelectrolyte in solution. The periodicity of the oscillations, as a function of concentration, indicates that at large surface separations the polymer chains are ordered as a nonintermixing, space-filling, latex. At polymer concentrations of between 200 and 1000 ppm, a transition to a system of ordered rods, parallel to the interface was seen for the final layer of polymer molecules.

Light Scattering of Dilute Hydrophobically Modified Alkali-Soluble Emulsion Solutions: Effects of Hydrophobicity and Spacer Length of Macromonomer

A novel comb water-soluble associative polymer (hydrophobically modified alkali-soluble emulsion (HASE)), comprising of a random copolymer of methacrylic acid (MAA), ethyl acrylate (EA), and 1 mol % of hydrophobically modified macromonomers, was studied using laser light scattering and rheological techniques. The hydrophobic substituents are separated from the backbone by a poly(ethylene glycol) (PEG or PEO) spacer chain. The hydrophobicity of the hydrophobic substituents and the length of PEO spacers control the microstructure of the aggregates or clusters. In dilute solution regime, the relaxation times of both unimers and aggregates are almost independent of hydrophobic groups and PEO spacer length. The aggregates are formed via the closed-association mechanism, and the balance of electrostatic and hydrophobic interactions controls their microstructures. However, by varying the hydrophobicity and the length of the PEO spacer chains, the internal conformation of the aggregates changes. Results from stat...

Light scattering from nonequilibrium concentration fluctuations in a polymer solution

We have performed light-scattering measurements in dilute and semidilute polymer solutions of polystyrene in toluene when subjected to stationary temperature gradients. Five solutions with concentrations below and one solution with a concentration above the overlap concentration were investigated. The experiments confirm the presence of long-range nonequilibrium concentration fluctuations which are proportional to (∇T)2/k4, where ∇T is the applied temperature gradient and k is the wave number of the fluctuations. In addition, we demonstrate that the strength of the nonequilibrium concentration fluctuations, observed in the dilute and semidilute solution regime, agrees with theoretical values calculated from fluctuating hydrodynamics. Further theoretical and experimental work will be needed to understand nonequilibrium fluctuations in polymer solutions at higher concentrations.

Excluded volume scaling for polymers

The excluded volume of several polymers in the dilute solution regime is calculated using the Monte Carlo integration. The calculated scaling exponent, λ, for the excluded volume for a polymer chain with another chain of the same length is 1.74±0.02. This exponent is consistent with the idea that the interaction of chains with one another in a good solvent is similiar to the interaction of two hard spheres. The effective radius of the hard sphere is proportional to the radius of gyration which has a scaling exponent of ν=0.595±0.005. This result is close to the theoretical value of 0.589. This study establishes the relationship λ=3ν.

Small-Angle Neutron Scattering Studies of Low Polarity Telechelic Ionomer Solutions. 2. Single Chain Scattering

A direct probe of the single chain conformation in associating low polarity model telechelic ionomer solutions has been obtained using small-angle neutron scattering. A contrast matching technique was employed utilizing a solution of hydrogenated and deuterated ionomer chains in a mixture of labeled and unlabeled solvent molecules. The scattering data at all concentrations and ionic levels examined show an excellent fit to the wormlike chain model. Single chain scattering patterns were obtained for two sodium-neutralized carboxy−telechelic polystyrene ionomers that differ by a factor of 2 in their molecular weight, in a concentration range from the dilute to the concentrated solution regime. The single chain dimensions were found to be influenced by both the ionic interactions and the extent of association. Both ionomer systems showed a contraction of the chain dimensions in the dilute solution regime which is more pronounced for the lower molecular weight telechelic ionomer. As concentration increases, the single chain dimensions increase until they reach a plateau value in the concentrated solution regime. This plateau value is very close to the chain dimensions of the ionomer in the bulk, as was found from a previous SANS study on similar ionomer systems. This plateau value chain dimension is also the same as the unperturbed dimension of the nonionic parent polymer in the bulk. The effect of concentration on the ionomer chain dimensions is attributed to the influence of ionic interactions as the nonionic form of the material shows larger chain dimensions in the concentration regime studied. These results indicate that intramolecular interactions with the formation of self loops prevail in the dilute solution regime. Intermolecular interactions with ionic groups connecting to different chains prevail in the concentrated solution regime, as evidenced by an extension of the chain dimensions.

Physical and structural properties of barley (1→3),(1→4)-β-D-glucan—III. Formation of aggregates analysed through its viscoelastic and flow behaviour

The Theological properties (flow and viscoelastic) of barley β-glucan in aqueous solution have been studied. The results shed light on the association behaviour of these macromolecules and even on the formation of network-like structures under certain circumstances. The concentrations used for this study were both in the dilute and in the semidilute regime, close to the critical value where overlap of macromolecular coils sets in. However, the association behaviour detected in such a regime and together with the present experimental techniques, agrees with previous results obtained with other techniques such as capillary viscometry and light scattering, which operate in the dilute solution regime, where no overlapping of the chains is expected. The influence of the molecular weight of the samples, the temperature and the ionic strength on the flow and oscillatory shear measurements has been studied. The preparation of samples and their thermal history have proved to be important factors in the development of associated structures, both affecting the results.

Light Scattering Studies of Block Ionomer Aggregation Characteristics in Nonpolar Solvent

In the dilute solution regime (1-5 mg/mL), the solution behavior of poly(tert-butylstyrene)-b-lightly sulfonated polystyrene (sodium neutralized with a 2.3 mol % sulfonation content) dissolved in cumene was compared with that of the parent neutral copolymer. For the block ionomer studied, reverse aggregates with the salt groups in the interior were obtained as expected. However, in all cases, a dominating portion of single chains (∼ 83 wt %) and a small amount of reverse aggregates (∼ 17 wt %, each aggreate consisting of, on average, about 10 unimers) coexist in a nearly constant weight ratio

ON ANOMALOUS DIFFUSION OF GROWING CLUSTERS

A continuous random walk of a growing cluster of dimension df is studied. It is assumed that its behavior is represented by a standard diffusion equation. A diffusion coefficient is assumed to be a cluster mass dependent power function which in the dilute solution regime takes a form first suggested by Kirkwood. The mass of the cluster increases in time according to another power law. It results in anomalous diffusion of the cluster in a three dimensional space which, in a linear case, is manifested by either power or logarithmic law of the mean square displacement. Some interesting examples and realizations of that process in polymer science, colloid physicochemistry or materials science are pointed out.

Block copolymer ionomers: solution behavior of lightly sulfonated polystyrene-b-poly(tert-butylstyrene) in polar solvent

Light scattering experiments were performed to study the structure and dynamics of block polystyrene-b-poly(tert-butylstyrene) copolymers in the sodium form with a sulfonation level of 5.8 and 12.0 mol % dissolved in DMAc at 25, 45, and 60°C in the dilute-solution regime. A polyelectrolyte-like solution behavior win observed. Due to the repulsive electrostatic interactions between like charges, the scattered intensities monitored were greatly reduced in compared with those of the unmodified diblock copolymer. In particular, a characteristic bimodal relaxation mode was observed on block ionomer solutions in strong contrast to the single-exponential decay found for the parent (neutral) copolymer solutions

Heat capacity of poly (ethylene glycol)-water mixtures: Poly (ethylene glycol)-water interactions

The specific heat capacity of the poly(ethylene glycol)-water system has been determined using a drop calorimeter over the full range of composition at 25 °C. The system heat capacity responds linearly to change in composition in the dilute solution regime up to 30% (w/w) and is an irregular function at lower water content. The breakpoint in solubility corresponds to a minimal content of 2.5 water molecules per ethylene oxide to complete hydration. We have difficulty in explaining the large excess heat capacity by the presence of a stoichiometrically defined hydrogen-bonded complex between each ethylene oxide group and water molecules. It seems possible that the water of hydration also interacts with bulk water and/or the rest of the polymer chain.

Viscometric determination of compatibility in PVC/ABS polyblends—II. Reduced viscosity-concentration plots

The variation of reduced viscosity (η sp/C) with concentration has been studied for PVC, ABS and a (50:50) blend of PVC/ABS in methyl ethyl ketone (MEK) at 30°C. The presence of a sharp crossover and a consequent reduction of slope in the (η sp/C) vs C plot of a blend signifies incompatibility between its constituents. A compatible polyblend, on the other hand, should not exhibit crossover when passing from the dilute solution regime to the semi-dilute regime and the viscosity can be predicted from the additivity law. Results now given for PVC/ABS give evidence for their compatibility. Toughening of rigid PVC by blending with ABS can be attributed to their mutual compatibility.