Measuring the size of polymers with negative radii using MALS/QELS: an exploration of the thermodynamic radius

The concept of 'size' in polymer science can have several interpretations, including definitions that rely on either statistical or equivalent-hard-sphere measures of the spatial extent of macromolecules in solution. A definition such as that of the equivalent thermodynamic radius (R(T)), which relies on the second virial coefficient of the polymer solution, offers the possibility of a zero or even a negative size parameter for macromolecules, depending on whether the polymer solution is in a theta or poor thermodynamic state, respectively. Here, we present the results of multi-angle light scattering measurements of R(T) for polystyrene and poly(methyl methacrylate), showing positive, negative, and zero values for this radius, depending on dilute solution thermodynamics. These results are augmented with measurements of the hydrodynamic radius, using quasi-elastic light scattering, and with random-walk-based calculations of the root-mean-square and viscometric radii. Re-examination of the literature provides additional examples of negative radii of polymers and oligomers.     

疏水缔合聚丙烯酰胺在盐水中的自组装行为

使用静态光散射、动态光散射以及原子力显微镜(AFM)研究了疏水缔合聚丙烯酰胺(HAPAM)在盐水溶液中的自组装行为.研究了聚合物分子在不同盐浓度中的表观重均分子量(Mw,a),均方根回转半径(),流体力学半径(),第二维里系数(A2)的变化,并根据/的比值得出聚合物分子的聚集形态.实验结果表明:随着盐浓度的增强,聚合物溶液的分子链由舒展变得卷曲.     

Conformations of sodium poly(styrene-4-sulfonate) macromolecules in solutions with different ionic strengths

Translational friction and viscosity of dilute solutions of sodium poly(styrene-4-sulfonate) with molecular masses of M = (5 × 10⁴)−(85 × 10⁴) are studied at different concentrations of low-molecular-mass salts. Molecular masses of the polymer are determined from the sedimentation-diffusion data. The study of the correlation between molecular masses and hydrodynamic characteristics resulted in ascertainment of the Kuhn-Mark-Houwink-Sakurada relationships for salt-free aqueous solutions of the polymer and solutions of the polymer in 0.2 M NaCl, 4.17 M NaCl, and 1.0 M KCl. It is shown that, as the ionic strengths of solutions are varied from minimum (H₂O) to maximum (4.17 M), macromolecules of the strong polyelectrolyte sodium poly(styrene-4-sulfonate) change their conformations from rigid rods to coils and, then, approach a globular conformation. In terms of the Gray-Bloomfield-Hearst and Yamakawa-Fujii theories and within the framework of the weakly bent cylinder model, the statistical Kuhn segment length and the hydrodynamic diameter of sodium poly(styrene sulfonate) chains are estimated in 0.2 and 4.17 M NaCl, 1.0 M KCl, and salt-free aqueous solutions. The electrostatic component of the equilibrium rigidity is taken into account within the framework of the Odijk-Fixman-Skolnick and Dobrynin theories.     

水溶性高聚物聚丙烯酰胺的稀溶液性质(Ⅰ)

本工作利用光散射和粘度方法,使用辐射聚合聚丙烯酰胺(PAAM)的级分样品,研究了在较宽分子量范围(10~4-10~7)内PAAM的特性粘数,分子尺寸及第二维利系数对重均分子量的依赖性.从实验上得到了PAAM在0.2mol/lNaCl水溶液中的均方旋转半径与均方末端距之间的关系及高分子-溶剂相互作用参数.     

Counterion adsorption theory of dilute polyelectrolyte solutions: apparent molecular weight, second virial coefficient, and intermolecular structure factor

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.     

Effect of NaCl on the self-aggregation of n-octyl beta-D-thioglucopyranoside in aqueous medium

This report investigates the effect of sodium chloride (NaCl) on the micellization, surface activity, and the evolution in the shape and size of n-octyl beta-D-thioglucopyranoside (OTG) aggregates. By using surface tension measurements, information was obtained on both changes in the critical micelle concentration and adsorption behavior in the air-liquid interface with the electrolyte concentration. These data were used to obtain the thermodynamic properties of micellization along with the corresponding adsorption parameters in the air-liquid interface. From extended static and dynamic light scattering measurements, the micelle molecular weight, the mean aggregation number, and the second virial coefficient, the apparent diffusion coefficient and the mean hydrodynamic radius of micelles in a range of NaCl concentrations were obtained. The light scattering data have shown that when the surfactant concentration is lower to 4.5 g/L, only spherical micelles are formed. However, an increase in the surfactant concentration induces an increase in micellar size, suggesting a rodlike growth of the micelles. This deviation of micelle geometry from spherical to rodlike is supported both by the ratio between the hydrodynamic radius and the radius of gyration and by the angular dependence of light scattering. On the other hand, the studies performed in the presence of high NaCl concentration (0.2 and 0.5 M) provide strong support for the view that the micelles may overlap together to form an entangled network above certain crossover concentration.     

Sedimentation equilibrium in nonideal heterogeneous systems. I. Fundamental equations for heterogeneous solute systems and some preliminary results

The sedimentation-equilibrium method is extended to treat nonideal solutions of heterogeneous macromolecules. The solute is assumed to be heterogeneous not only in molecular weight but also in other quantities such as partial specific volume, second virial coefficient and specific refractive increment. General expressions for various observable molecular weights, especially for weight-average, z-average, and number-average molecular weights, are derived. Their dependences on sedimentation parameter and solute concentration are discussed in detail. For the extrapolation of observable molecular weights, giving a type of weight-average, and z-average, to infinite dilution to estimate the molecular weight and the second virial coefficient, average concentration is superior as a concentration variable to original concentration. The plots of observable molecular weight versus average concentration are usually less influenced by the choice of the sedimentation parameter, especially of rotor speed. The general expressions are applied to a few special cases; monodisperse polymer, polydisperse homologous polymer, and polymer blend. The results are compared with experiments on a monodisperse, polystyrene, a polydisperse poly(methyl methacrylate), and a mixture of the two polymers, all in 2-butanone at 25°C. The agreement between the theory and experiments is satisfactory.     

Effect of Chemical Structure and Charge Distribution on Behavior of Polyzwitterions in Solution

Summary: The hydrodynamic and conformational properties of polyelectrolyte poly(N,N-diallyl-N,N-dimethylammonium chloride) and its corresponding polybetaine poly(2-diallyl(methyl)ammonio)acetate) molecules in aqueous solutions with various ionic strength and pH, were studied by viscometry, static and dynamic light scattering methods. It was established that a 1 M NaCl solution is a thermodynamically good solvent for poly(N,N-diallyl-N,N-dimethylammonium chloride). In water solutions conformation of poly(2-diallyl(methyl)ammonio)acetate) molecules corresponds to polymer coil under θ–conditions. An increase in the concentration of NaCl in water and 0.1M NaOH solutions from 0 to 1 mol/l brings about a sharp gain in the intrinsic viscosity of the polymer and in the hydrodynamic radius of molecules. This effect results from the decomposition of zwitterion pairs responsible for the compact conformation of polymer molecules in water and 0.1 M NaOH. The Kuhn segment length for poly(2-diallyl(methyl)ammonio)acetate) molecules A = 6.3 nm determined in water and in 0.1 M NaOH solutions practically coincided with A value 6.6 nm, received in 1 M NaCl and in 0.1 M NaOH/1M NaCl. For poly(N,N-diallyl-N,N-dimethylammonium chloride) molecules in 1 M NaCl solutions A = 3.9 nm.     

Excluded volume study of a sulfonate-containing polyelectrolyte in salt solutions

Chain characteristics of a linear sulfonate-containing homopolymer, sodium poly(3-methacryloyloxypropane-1-sulfonate), in aqueous salt solutions (ionic strength, C_s = 0.01N to 5N NaCl) have been investigated by light scattering and intrinsic viscosity. The molecular weight (M?_w)–viscosity relation can be well described by the Mark–Houwink and the Stockmayer–Fixman equations. The coil is highly expanded even in the most concentrated NaCl solution (6N), and no 1:1 electrolyte was found to precipitate this polymer. A linear relation was observed between the viscosity expansion factor, α^3η, and (M?_w/C_s)^1/2. Examination of the data in terms of theories for excluded volume and hydrodynamic interaction suggests that the coil experiences dominant hydrodynamic interaction, corresponding to a nondraining coil, and the second virial coefficient and coil expansion at high C^s can be correlated by the Flory–Krigbaum–Orofino equation. Results for this polymer are compared with those for other polyelectrolytes, and are discussed in terms of chain structure, flexibility, and hydrophobicity.     

水溶性高聚物聚丙烯酰胺的稀溶液性质(Ⅰ)

 本工作利用光散射和粘度方法,使用辐射聚合聚丙烯酰胺(PAAM)的级分样品,研究了在较宽分子量范围(10⁴-10⁷)内PAAM的特性粘数,分子尺寸及第二维利系数对重均分子量的依赖性.从实验上得到了PAAM在0.2mol/lNaCl水溶液中的均方旋转半径与均方末端距之间的关系及高分子-溶剂相互作用参数.     

On the theory of dilute polyelectrolyte solutions: Extensions,refinements, and experimental tests

We synthesize a quantitative theory for the radius of gyration, second virial coefficient, intrinsic viscosity, and friction coefficient for polyelectroytes in dilute solution from existing treatments of electrostatic and hydrodynamic interactions within and among wormlike chains. Comparison with data for K-PSS demonstrates the importance of accounting for nonlinearities in the electrostatics and the finite diameter of the polymer backbone.     

Polymers containing quaternary ammonium groups based on poly(N-vinylimidazole)

A poly(N-vinylimidazole) (PNVI)—based poly(carboxybetaine) with two methylene groups between the opposite charges was achieved by the nucleophilic addition reaction of the mentioned aminic polymer to the carbon-carbon double bond of acrylic acid (AA). Treatment of poly(carboxybetaine) with concentrated HCl (2 N) for long time leads to the corresponding cationic polyelectrolyte. The poly(carboxybetaine) is soluble in both water and aqueous solutions of salts such as: LiCl, NaCl, NaHCO₃, CaCl₂, Na₂SO₄. In water and in the first three salts, poly(carboxybetaine) exhibits a non-polyelectrolyte behaviour (a linear dependence of reduced viscosities on polymer or salt concentration), while in the remaining two salts, a slight polyelectrolyte behaviour is observed. The cationic polyelectrolyte is soluble in water and aqueous solutions of LiCl, NaCl, CaCl₂ and NaHCO₃, except Na₂SO₄. It has a polyelectrolyte behaviour in all solutions. Also, the binding trends of the added salts by polymers are discussed.     

Dimensions of a free linear polymer and polymer immobilized on silica nanoparticles of a zwitterionic polymer in aqueous solutions with various ionic strengths

The dimensions and intermolecular interactions of a surface-grafted and unbound free polyampholyte, poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC), were estimated in aqueous solutions with various ionic strengths. Free linear PMPC was synthesized by atom-transfer radical polymerization (ATRP), and static light scattering (SLS) and dynamic light scattering (DLS) were carried out for the PMPC solutions with various concentrations of NaCl, c s. The hydrodynamic radius R H and the second virial coefficient A 2 of PMPC were independent of c s (0-0.5 M), though both R H and A 2 of polyampholytes usually strongly depend on the ionic strength. PMPC-immobilized silica nanoparticles (PMPC-SiNP) were also synthesized by surface-initiated ATRP, and DLS was carried out as for the solutions of linear PMPC to investigate the dependence of the dimensions of PMPC immobilized on a solid surface on the ionic strength. The molecular weight and surface density of PMPC immobilized on SiNP were estimated from the results obtained by GPC, NMR, and thermogravimetric analysis. The independence of R H of PMPC-SiNP was also observed, but its magnitude was larger than that of linear PMPC, although the molecular weight of PMPC immobilized on SiNP was smaller than that of linear PMPC. The larger dimension of PMPC immobilized on SiNP was explained by the excluded volume effect between the immobilized polymer chains.     

Synthesis and aqueous solution properties of sterically stabilized pH-responsive polyampholyte microgels

Emulsion copolymerization of poly(methacrylic acid) and poly(2-(diethylamino)ethyl methacrylate) (PMAA/PDEA) yielded pH-responsive polyampholyte microgels of 200-300 nm in diameter. These microgels showed enhanced hydrophilic behavior in aqueous medium at low and high pH, but formed large aggregates of approximately 2500 nm at intermediate pH. To achieve colloidal stability at intermediate pH, a second batch of microgels of identical monomer composition were synthesized, where monomethoxy-capped poly(ethylene glycol)methacrylate (PEGMA) was grafted onto the surface of these particles. Dynamic light-scattering measurements showed that the hydrodynamic radius, Rh, of sterically stabilized microgels was approximately 100 nm at intermediate pH and increased to 120 and 200 nm at pH 2 and 10, respectively. Between pH 4 and 6, these microgels possessed mobility close to zero and a negative second virial coefficient, A2, due to overall charge neutralization near the isoelectric pH. From the Rh, mobility, and A2, cross-linked MAA-DEA microgels with and without PEGMA retained their polyampholytic properties in solution. By varying the composition of MAA and DEA in the microgel, it is possible to vary the isoelectric point of the colloidal particles. These new microgels are being explored for use in the delivery of DNA and proteins.     

Solution characterization of poly(isobornyl methacrylate) in tetrahydrofuran

Thermodynamic and hydrodynamic properties of dilute solutions of poly (isobornyl methacrylate) (PIMA) in tetrahydrofuran (THF) were characterized by using viscosity, static, and dynamic light scattering measurements. PIMA samples with different molecular weight were obtained by fractional precipitation of PIMA solution. Chain dimension parameters (R_g and R_H), together with second virial coefficient A₂ and intrinsic viscosity [η], were used to calculate various solution parameters characterizing polymer chains in polymer solutions. The experimental results are compared with calculation, indicating that PIMA behaves as a flexible coil in THF. © 1994 John Wiley & Sons, Inc.     

Substrate concentration dependence of the diffusion-controlled steady-state rate constant

The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B2*. Comparisons to Brownian dynamics simulations excluding hydrodynamic interactions show excellent agreement up to bulk number densities of B2*rho0 < approximately = 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.     

Rheological Behavior and Scattering Studies of Acrylamide-Based Copolymer Solutions

Summary: In this paper the chemical structure of an acrylamide-N,N-dihexylacrylamide copolymer was established by IR and NMR. Static and dynamic light scattering in formamide were used in order to evaluate the polymer structural parameters, such as weight-average molecular weight (M_w), second virial coefficient (A₂), radius of gyration (R_G), the form factor P(q) and the hydrodynamic radius (R_H). Additionally to the classical characterization, those results indicated the presence of aggregation, showing that formamide is not a very good solvent, as stated in earlier investigations. The rheological behavior in aqueous solutions was evaluated as a function of the salt concentration. The solutions presented an important viscosity increase in the presence of NaCl and did not show any sensitivity to the presence of CaCl₂. This result is in favor of the oil recovery especially in high salinity reservoirs.     

Effect of molecular dimensions of components on phase transitions in solutions of oligomeric polyethers

The molecular masses and intrinsic viscosities of a series of oligomeric poly(propylene glycols) have been studied by light scattering, analysis of chain ends, viscometry, and the cloud-point method. Phase diagrams are plotted and the Flory-Huggins thermodynamic interaction parameters and the second virial coefficients are calculated for oligomeric poly(propylene glycol)-n-alkane systems. The effects of the molecular dimensions of components on their mutual solubility and positions of boundary curves are determined. UCST decreases with an increase in the size of poly(propylene glycol) macromolecules and increases with an increase in the size of n-alkane molecules.     

Molecular properties of the copolymers of <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-diallyl-<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dimethylammonium chloride and maleic acid

The hydrodynamic and conformational properties of molecules of poly(N,N-diallyl-N,N-dimethylammonium chloride) and N,N-diallyl-N,N-dimethylammonium chloride-maleic acid copolymers of different compositions in solutions with various ionic-strength and pH values, as well as of the polyelectrolyte complex based on the copolymer with dodecyl sulfate anions in chloroform, are studied. For poly(N,N-diallyl-N,N-dimethylammonium chloride) molecules in a 1 M NaCl solution, the Kuhn segment length and the hydrodynamic diameter of the chain are estimated as A = 3.9 nm and d = 0.48 nm, respectively. In acidic solutions with pH 3.5, the copolymers demonstrate behavior typical for polyelectrolytes. In an alkaline solution with pH 13, when 1 M NaCl is added to the solution of the copolymer containing 29 mol % maleic acid units, there is an antipolyelectrolyte effect that manifests itself as an increase in the intrinsic viscosity of the copolymer and in the hydrodynamic radius of its molecules. It is found that an increase in the fraction of maleic acid units in the copolymer from 12 to 42 mol % brings about a reduction in the equilibrium rigidity of its macromolecules from 4.1 to 2.2 nm. The equilibrium rigidity of polyelectrolyte-complex molecules is higher than that of initial copolymer molecules owing to steric interactions arising between the aliphatic chains of dodecyl sulfate anions. In an electric field, the molecules of the complex are oriented owing to the induced dipole moment resulting from the displacement of dodecyl sulfate anions along the chain contour.     

Effective size and fractal dimension of polyelectrolytes determined by diffusion NMR

Polyelectrolytes are macromolecules containing dissociable or charged groups on the main chain or in side groups. These charges are the basis of the water solubility of polyelectrolytes. The solution properties namely the conformation is determined by an interplay of thermodynamic and electric interactions. The electrostatic interaction is influenced by the ionic strength of the solution. As a measure of the effective size of the macromolecules the hydrodynamic radius is determined from the self-diffusion coefficient measured via pulsed- field gradient nuclear magnetic resonance. From variation of the hydrodynamic radius with molecular weight for each ionic strength, the fractal dimension has been determined for the example of poly(styrenesulfonate). With increasing ionic strength the fractal dimension, which describes the use of space for the fictitious growth of the molecule when increasing the molecular weight, increases. This implies a denser packing of the molecules in higher ionic strength.