From small charged molecules to oligomers: a semiempirical approach to the modeling of actual mobility in free solution

According to Stokes' treatment, the ionic mobility of particles, which are small with respect to Debye length, is usually considered to be proportional to the nominal charge and inversely proportional to the hydrodynamic radius. Experimentally, it is well known, however, that the ionic mobility of a small multicharged molecule does not depend linearly on its nominal charge in a wide range. This behavior can be accounted for by a condensation of the charge or a modification of the friction coefficient with the charge. This paper presents a semiempirical modeling of the actual mobility based on the assumption of additivity of frictional contributions pertaining to the uncharged molecular backbone and to each charged or uncharged moiety. Condensation of the charge was not considered. The model first appeared to be suitable for multicharged analytes having a characteristic dimension smaller than the Debye length, such as benzene polycarboxylic acids and polysulfated disaccharides. This approach was then adapted to account for the actual mobilities of singly and evenly charged oligomers (N-mers) having a dimension smaller than or similar to the Debye length. Rather good experimental agreement was obtained for polyalanines and polyglycines (N < or = 6), fatty acid homologs, fully sulfonated polystyrene oligomers (N < or = 13), and polycytidines (N < or = 10). Especially the influence of the polymerization degree on the mobility of oligomers having identical charge densities was clarified. It is also shown that the electrophoretic contribution to the overall friction coefficient increases linearly with the nominal charge but hardly depends on the chemical nature of the charged moieties. This model should be of interest to evaluate the role of various physicochemical phenomena (hydrodynamic and electrophoretic frictions, hydrodynamic coupling, charge condensation) involved in the migration of charged oligomers.     

On the use of the activation energy concept to investigate analyte and network deformations in entangled polymer solution capillary electrophoresis of synthetic polyelectrolytes

The activation energy associated with the electrophoretic migration of an analyte under given electrolyte conditions can be accessed through the determination of the analyte electrophoretic mobility at various temperatures. In the case of the electrophoretic separation of polyelectrolytes in the presence of an entangled polymer network, activation energy can be regarded as the energy needed by the analyte to overcome the obstacles created by the separating network. Any deformation undergone by the analyte or the network is expected to induce a decrease in the activation energy. In this work, the electrophoretic mobilities of poly(styrenesulfonates) (PSSs) of various molecular weights (Mr 16 x 10(3) to 990 x 10(3)) were determined in entangled polyethylene oxide (PEO) solutions as a function of temperature (in the 17-60 degrees C range) and the PSS activation energies were calculated. The influences of the PSS molecular weight, blob sizes zetab of the separating network (related to the PEO concentration), ionic strength of the electrolyte and electric field strength (75-600 V/cm) were investigated. The results were interpreted in terms of analyte and network deformations and were confronted with those previously obtained for DNA migration in polymer solutions and chemical gels. For a radius of gyration Rgzetab, suggesting PSS and network deformations in the latter case. Increasing ionic strength resulted in an increase in the PSS activation energy, because of the decrease of their radii of gyration, which makes them less deformable. Finally, the activation energies of all the PSSs are a decreasing function of field strength and at high field strength tend to reach a constant value close to that for a small molecule.     

Electrophoretic mobility of concentrated spheres with a charge-regulated surface

The electrophoretic behavior of a concentrated spherical colloidal particle is modeled theoretically under the Debye-Hückel condition. The surface of a particle contains dissociable functional groups, the dissociation of which yields negative fixed charges. The model derived is applicable to an arbitrarily thick double layer. We show that the absolute surface potential decreases with the increase in kappa(a); kappa and a are the reciprocal Debye length and the radius of a particle, respectively. Moreover, the variation of the absolute electrophoretic mobility as a function of kappa(a) has a maximum.     

Preparation of raspberry-like silica microcapsules via sulfonated polystyrene template and aniline medium assembly method

Raspberry-like composite particles and microcapsules were prepared with anionic sulfonated polystyrene (PSS) particles as templates and cationic aniline monomer as assembly medium. With the help of the sulfonated microgel shells, aniline and silica particles could not only adsorbed onto template surfaces but also go inward shells and finally form microcapsules with varied silica shell thickness. The sulfonation extent of PSS particles first climbed up and then decreased with sulfonation time due to the competition of sulfonation reaction and PSS chain detachment. The silica content in composite particles and shell thickness of microcapsules followed similar trend with sulfonation extent. The choice of aniline as assembly medium was checked by comparing with methyl methacrylate and [2-(methacryloyloxy) ethyl] trimethylammonium chloride, and it was found that the cationic and water-insoluble properties of aniline are both important for the composite efficiency.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

PBMA-b-PSt磺化嵌段离聚体在DMF溶液中的聚集行为

采用激基缔合物荧光光谱法研究了轻度磺化聚甲基丙烯酸丁酯－b－聚苯乙烯（PBMA-b－PSt）嵌段离聚体在极性溶剂N，N－二甲基甲酰胺（DMF）溶液中的聚集行为；发现嵌段离聚体的磺化度和浓度强烈影响溶液中聚合物链的聚集态结构，不同的磺化度样品具有不同的临界聚集浓度；随磺化度增加，聚合物链缠绕密集，形成具有多苯环的聚集体，而且当磺化度为摩尔分数x＝3．59％时，荧光发射光谱最大发射峰波长出现最大红移，临界聚集浓度最低，说明最容易形成多苯环聚集体，该磺化点可以认为是磺化聚甲基丙烯酸丁酯－b－聚苯乙烯体现离聚体行为和聚电解质行为的临界磺化度。     

Sulfonation of polystyrene: Toward the “ideal” polyelectrolyte

Sulfonation of narrow polydispersity polystyrene, PS, standards remains the method of choice for generating polystyrene sulfonate, PSS, samples with defined composition. Although a variety of sulfonation techniques have been described, relatively little is reported on the material obtained, which is used for so many studies on the fundamental behavior of polyelectrolytes. Here, we show that powdered polystyrene treated with concentrated sulfuric acid (96%) at 90 °C without catalyst yields fully sulfonated PSS. Extensive characterization with ¹H and ¹³C NMR as well as size exclusion chromatography coupled with static and dynamic light scattering shows no evidence of sulfone crosslinking or chain degradation under the conditions used. Though mono‐sulfonated as soon as it dissolves in the acid, the PSS contains about 6% meta substitution. Sulfonation kinetics for this heterogeneous reaction depend strongly on particle size, sulfuric acid content and temperature. For preparing perdeuterated PSS from the corresponding PS it is essential to employ D₂SO₄, as about half of the aromatic units undergo H/D exchange during sulfonation. The remaining ortho H/D may be exchanged with extended exposure to the concentrated sulfuric acid, but the meta site is deactivated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2416–2624     

Morphological studies and ionic transport properties of partially sulfonated diblock copolymers

The morphological behavior of partially sulfonated polystyrene-block-poly(ethylene-alt-propylene) (PS-PEP) membranes cast from tetrahydrofuran (THF) solutions were investigated by small-angle X-ray scattering (SAXS) and atomic force microscopy (AFM).The uptakes of methanol and water increase as the sulfonation degree increases, the methanol uptake being overwhelmingly greater than the water uptake. The conductivity increases almost exponentially with increasing sulfonation degree of polystyrene units. Clusters of sulfonated units that are formed in the solution used for casting membranes persist in the solid state after evaporation. In contact with water, swelling of the membranes proceeds predominantly in these clusters. The original lamellar morphology of the diblock copolymer is progressively deformed with increasing degree of sulfonation by the presence of the clusters containing ion-rich sequences of sulfonated polystyrene blocks.     

The influence of secondary interactions during the formation of polyelectrolyte multilayers: layer thickness, bound water and layer interpenetration

With X-ray and neutron reflectivity, the structure and composition of polyelectrolyte multilayers from poly(allyl amine) (PAH) and poly(styrene sulfonate) (PSS) are studied as function of preparation conditions (salt concentration and solution temperature, T). The onset of a temperature effect occurs at 0.05 M NaCl (Debye length approximately 1 nm). At 1 M salt, the film thickness increases by a factor of 3 on heating the deposition solution from 5 to 60 degrees C. The PAH/PSS bilayer thickness is independent of the kind of salt (NaCl or KCl), yet its composition is different (more bound water for NaCl). At low T, the internal roughness is 33% of the bilayer thickness; it increases to 60% at high T. The roughening is accompanied by a total loss of bound water. At which temperature the roughening starts is a function of the kind of salt (50 degrees C for NaCl and 35 degrees C for KCl). The strong temperature dependence and the eventual loss of bound water molecules may be attributed to the hydrophobic force; however, there is an isotope effect, since the loss of bound water is less pronounced in the deuterated layers.     

Electrophoresis of concentrated mercury drops

The electrophoretic behavior of concentrated monodispersed, positively charged mercury drops is investigated theoretically. The present study extends previous analyses by considering arbitrary surface potentials, double-layer polarization, and the interaction between adjacent double layers. The coupled equations describing the spatial variations in the flow field, the electric field, and the concentration field are solved by a pseudo-spectral method. For a low surface potential phi(r), the mobility increases monotonically with kappaalpha; kappa and alpha are respectively the reciprocal Debye length and the radius of a mercury drop. For medium and high phi(r), the mobility curve has a reflection point, which arises from the interaction of adjacent double layers, for kappaalpha. Also, if phi(r) is high, the mobility curve may exhibit a local minimum as kappaalpha varies. This phenomenon is pronounced if the concentration of the dispersed phase is high. If the double layer is thick, the mobility increases with phi(r), and the reverse is true if it is thin. We show that the higher the concentration of the dispersed phase the smaller the mobility, and as kappaalpha becomes large the mobility approaches a constant value, which is independent of the concentration of the dispersed phase. The mobility of mercury drops is larger than that of the corresponding rigid particles.     

Theory of electrophoretic mobility of polyelectrolyte chains

An explicit formula is derived for the electrophoretic mobility of a linear polyelectrolyte chain in terms of the molecular weight, Debye length and solvent quality. The nature of the crossover between different regimes as the salt concentration and molecular weight are varied is presented. The effect of chain statistics intermediate between the Gaussian and rodlike limits on the electrophoretic mobility is analysed for the first time.     

Electrophoresis of soft particles: analytic approximations

An approximate analytic expression is derived for the electrophoretic mobility of a weakly charged spherical soft particle (i.e., a hard particle covered with a weakly charged polyelectrolyte layer) on the basis of the general mobility expression for soft particles (Ohshima, H., J. Colloid Interface Sci. 2000, 228, 190-193). The obtained mobility expression, which reproduces various approximate results so far derived and gives some new mobility formulas, covers all types of weakly charged soft particles with arbitrary values of the thickness of polymer layer, the radius of the particle core, the electrophoretic softness, and the Debye length, including spherical polyelectrolytes with no particle core as well as spherical hard particles with no polyelectrolyte layer.     

Water vapor sorption and diffusion in sulfonated aromatic polyamides

In this contribution polyamides with different sulfonation degrees were directly synthesized from a combination of sulfonated and nonsulfonated diamines and isophthaloyl chloride. They were then used as dense membranes to study water sorption and mass transport properties. The polymers were characterized by their inherent viscosity and by spectroscopic methods, and the water vapor unsteady sorption phenomena were studied using a gravimetric technique. The effect of sulfonation substitution concentration in these polymers produces very interesting and original results in a number of properties such as the ionic exchange capacity, water equilibrium sorption and diffusivity. Obtained results are discussed and explained in the light of existing theories. Sorption behavior for polymers with a low sulfonation degree, up to 30%, can be explained with Langmuir equation. With larger substitution degree (40 and 60%) an additional mechanism must be assumed to explain sorption data. Assuming the presence of two phases helps to explain the observed diffusivity results. The mass transport mechanism is assumed to be Fickian. When water activity is low diffusivity systematically decreases as the degree of sulfonation increases. However, as water activity increases less sulfonated and nonsulfonated (PA0, PA20 and PA30) behave completely different from PA40 and PA60. The first group of polymers shows a tendency to decrease the rate of diffusion as water activity increases while the second group shows the opposite behavior, with a maximum in diffusivity at intermediate water activities. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2007–2014, 2007     

Sulfonation of a flexible and unexpected electrically conductive polysulfone and its performance in perovskites solar cells

The effect of sulfonation on polysulfone regarding its electrical properties is studied and discussed. In addition to the effect of percentage of sulfonation, the thickness of thin films and the ultraviolet (UV) treatment also were evaluated and reported. The results indicate that percentage of sulfonation is the most important effect, even over thickness. As the sulfonation percentage was increased, better electrical performance (fill factor and power conversion efficiency) was obtained because the sulfonate groups impart a kind of vacancy into the polymer structure, showing comparable energy level to that of conventional poly (3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS).In addition, the UV treatment not only cleans the film's surface but also polarizes the polymeric's surface improving the polysulfone performance, which was 24% better, at least, respect to that obtained without UV treatment. The obtained results open the possibility to optimize sulfonated polysulfones that could be used in inverted hybrid perovskite solar cells.     

Preparation,characterization and ion adsorption properties of functionalized polystyrene modified with 1,4-phenylene diisocyanate and diethylenetriamine

In the present work, linear polystyrene (PS) was functionalized by a sulfonation reaction providing sulfonated polystyrene (PSS). Then, the PSS polymer chains were cross-linked with the 1,4-phenylene diisocyanate (PPDI) group in tetrahydrofuran (THF), which led to a PSS-PPDI polymer. The PSS-PPDI was grafted by diethylenetriamine (DETA) in a solution of THF to obtain polymer PSS-PPDI-DETA. Their structures were characterized by infrared spectroscopy (ATR-FTIR), elemental analysis (EA), differential scanning calorimetry (DSC), thermogravemetric (TGA), thermodynamic (DTA) and differential thermogravimetric (DTG) analysis. Subsequently, the obtained polymers were tested for their ability to remove some metal ions from aqueous media such as Zn²⁺, Cd²⁺ and Co²⁺.     

Synthesis and characterization of multiblock sulfonated poly(arylene ether sulfone) membranes with different hydrophilic moieties for application in polymer electrolyte membrane fuel cell

Multiblock sulfonated poly(arylene ether sulfone)s were synthesized to investigate the structural effects on their membrane properties. Three different types of sulfonated hydrophilic blocks were used; their structures possessed different acidity and local concentration of sulfonic acid groups. For the comparison between the block copolymers, a hydrophobic block with the same chemical structure and block length was used. The different acidities and local concentration were achieved using different sulfonation methods, such as postsulfonation and direct condensation with sulfonated monomers, and different monomers for preparing the hydrophilic block. The higher acidity and concentration of sulfonic acid groups resulted in higher proton conductivity under certain relative humidity conditions and phase separation as shown in the transmission electron microscopy analysis. The synthesized oligomers and polymers were well characterized, and the other physical properties were also investigated. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2947–2957     

Effects of dielectric gradients-mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric-mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core-soft shell representation is not appropriate.     

Macromolecular dynamics of sulfonated poly(styrene-b-ethylene-ran-butylene-b-styrene) block copolymers by broadband dielectric spectroscopy

Macromolecular dynamics of sulfonated poly(styrene-b-ethylene-ran-butylene-b-styrene) (sSEBS) triblock copolymers were investigated using broadband dielectric spectroscopy (BDS). Two main relaxations corresponding to the glass transitions in the EB and S block phases were identified and their temperature dependences were VFT-like. T_g for the S block phase shifted to higher temperature due to restrictions on chain mobility caused by hydrogen bonded SO₃H groups. While the EB block phase T_g appeared to remain constant with degree of sulfonation in DMA experiments, it shifted somewhat upward in BDS spectra. A low temperature relaxation beneath the glass transition of the EB block phase was attributed to short range chain motions. The Kramers–Krönig integral transformation was used to calculate conductivity-free loss permittivity spectra from real permittivity spectra to enhance true relaxation peaks. A loss permittivity peak tentatively assigned to relaxation of internal S-EB interfacial polarization was seen at temperatures above the S block phase glass transition, and the temperature dependence of this relaxation was VFT-like. The fragilities of the EB and S block domains in sulfonated SEBS decreased after sulfonation. The temperature dependence of the dc conduction contribution to sSEBS loss spectra also followed VFT-like behavior and S block segmental relaxation time correlated well with conductivity according to the fractional Debye–Stokes–Einstein equation.     

Electrophoretic mobility of the polymer-like micelles of tetradecyldimethylamine oxide hemihydrochloride

Effects of the surfactant concentration C_d and the NaCl concentration C_s on the electrophoretic mobilities U of the well-characterized polymer-like micelles have been investigated by the electrophoretic light scattering, using tetradecyldimethylamine oxide hemihydrochloride (C14DMAO·1/2HCl). At the high ionic strength of 0.1 mol kg⁻¹ NaCl, the electrophoretic mobilities were independent of C_d (5 mM < C_d < 100 mM), despite the concentration-dependent micelle growth of the polymer-like micelles. This suggests that the electrophoretic mobility of the polymer-like micelle at high ionic strengths is independent of the contour length (i.e., the molecular weight), as found on linear polyelectrolytes. Somewhat surprisingly, the entanglements of the polymer-like micelles gave small effect on the electrophoretic mobilities in the examined range of the surfactant concentration above an overlap concentration. The mobilities of the polymer-like micelle decreased with √C_s in a single exponential manner in the range of C_s from 0.02 to 0.3 mol kg⁻¹. It is suggested that the cylinder model can be applied to the electrophoretic mobilities of the polymer-like micelles at high ionic strengths (i.e. a free-draining behavior), since the persistence length of the polymer-like micelle (20 nm) is much larger than the Debye length at high ionic strength.