Normal and shear forces between a polyelectrolyte brush and a solid surface

The diblock copolymer poly(methyl methacrylate)‐b‐poly(sodium sulfonated glycidyl methacrylate) (PMMA‐b‐PSGMA) was end‐attached by its hydrophobic block (PMMA) onto mica hydrophobized by a stearic trimethylammonium iodide (STAI) layer, to form a polyelectrolyte brush immersed in water. With a surface force balance (SFB), we extended earlier measurements between two such brush layers for the case of normal and shear forces at different shear rates, surface separation, and compressions between one mica surface coated with STAI or a STAI‐diblock layer against a bare mica surface. After coating one of the surfaces with STAI, a long range attraction that results in a jump into an adhesive flat contact between the hydrophobic and hydrophilic surfaces was observed. A very different behavior was seen after forming the polyelectrolyte brush on the STAI‐coated surface. The long range attraction was replaced by repulsion, accompanied by very low friction during shear (ca. three orders of magnitude lower than with adsorbed polyelectrolytes). On further compression, a weak attraction to the adhesive contact was observed. From the final surface–surface contact separation, we deduce that most of the polyelectrolyte diblock brush layer was squeezed out from the gap, leaving the STAI layer and a small amount of the polymer attached to the surface. Stick‐sliding behavior was seen while applying shear, suggesting a dissipation mechanism caused by the trapped polyelectrolyte. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 193–204, 2005     

Rheological properties of ionic and nonionic polyacrylamide solutions

Non-Newtonian shear viscosities were measured over six decades of strain rate k for 13 solutions of both the ionic and nonionic forms of polyacrylamide. By using the Weissenberg rheogoniometer with both the cone-and-plate and the parallel-plate attachments, the normal stress functions σ₁ (k²) and σ₂(k²) were obtained for four of the solutions. From the measurements of the shear viscosity and the normal stresses at low rates of strain, characteristic times τ and τ_N, respectively, were determined for each solution. The quantity τ was then used to nondimensionalize the strain rate τk, and when plotted versus the reduced shear viscosity, found successfully to correlate the experimental data for all the polyelectrolyte solutions over the entire range of τk and the data for the concentrated solutions of the nonionic polymer over a smaller range of τk. However, in order to correlate the normal stress data for the polyelectrolyte solutions, a second reduced strain rate (τ_Nk) was used. Thus, two different times were required to correlate all the observed data. The shear viscosity data for the dilute solutions of the nonionic polymer were well represented by the two-parameter, non-Newtonian intrinsic viscosity function that has been computed by Fixman.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Nonlinear dynamics of melted polymer layers

A theory for non-linear rheology of molten polymer layers between solid surfaces in the Rouse regime is discussed. It is shown that the effect of finite extensibility of polymer chains leads to the characteristic 1/3 power law for the shear stress vs. shear velocity in the regime of high velocities. It is also shown that bridging polymer fragments connecting the two surfaces play an important role for the rheology if the effective monomer friction in the immediate vicinity of the surfaces is much higher than far from the surfaces. In particular we predict that shear stress is decreasing with shear velocity u in a limited range between u₁ and u, _min. This effect results in a possibility of stick-slip periodical dynamics of the layer under a constant imposed velocity.     

Ac voltammetry studies of electron transfer kinetics for a redox couple attached via short alkanethiols to a gold electrode

Ac voltammetry (ACV) is used to determine the chain length dependence of electron transfer kinetics between gold bead electrodes and ruthenium redox centers attached to the electrode surface via short alkanethiols. The pentaamminepyridine ruthenium redox centers are attached to pre-assembled monolayers of mercaptoalkanecarboxylic acids (HS(CH₂)_mCOOH, m=5, 7, 10). Equations for faradaic admittance of strongly adsorbed, non-interacting electroactive species are fitted to the experimental faradaic admittance data. Kinetic heterogeneity is suggested to be a probable reason for the apparent increase in the standard rate constant (k_s) and decrease in the total coverage of redox centers (θ_total) as the perturbation frequency increases. Because of the frequency dependence of k_s and because of limitations in the correction for uncompensated resistance, faradaic admittance at a fixed phase angle of 70° is chosen to compare k_s for different chain lengths. The plot of ln(k_s) versus m (the number of methylene units) is linear with a slope of −1.2±0.1 per CH₂.     

Glass and Structural Transitions Measured at Polymer Surfaces on the Nanoscale

This paper reviews our recent progress in determining the surface glass transition temperature, T_g, of free and substrate confined amorphous polymer films. We will introduce novel instrumental approaches and discuss surface and bulk concepts of T_g. The T_g of surfaces will be compared to the bulk, and we will discuss the effect of interfacial interactions (confinements), surface energy, disentanglement, adhesion forces, viscosity and structural changes on the glass transition. Measurements have been conducted with scanning force microscopy in two different shear modes: dynamic friction force mode and locally static shear modulation mode. The applicability of these two nano-contact modes to T_g will be discussed.This revised version was published online in November 2005 with corrections to the Cover Date.     

Molecular Weight Development of Surface and Solution Polymers in Surface‐Initiated Atom Transfer Radical Polymerization and Their Dependence on Radical Termination Modes

In the surface‐initiated atom transfer radical polymerization, the polymerization proceeds both in solution and on surface. This work reports a modeling study, describing the growth of the molecular weight and polydispersity of polymer both on surface and in solution. It is found that both surface radical termination and solution monomer consumption significantly suppress the growth rate of polymer layer. Besides, the former affects the molecular weights of polymer both on surface and in solution. If the termination rate constant in solution (k_t,sol–sol) is the same as that of surface and solution interfaces (k_t,sol–surf), and the surface termination (k_{t,surf–surf}) is negligible, then the polymers both on surface and in solution have the same molecular weight. However, if surface radicals terminate among themselves, the molecular weight of polymer on surface will lower than that in solution. Such termination is promoted by surface radical migration through activation/deactivation reactions in solution. When k_t,sol–surf <k_t,sol–sol, the molecular weight of surface polymer becomes higher than that in solution. This situation is resulted from surface radical trap due to a high grafting density.

     

Kinetic model of living radical polymerization

This work studies the kinetics of living radical polymerization by means of both the nonsteady state approach and the quasi-stationary state method. Expressions for the numberand weight-average degress of polymerization and the polydispersity index were derived. Numerical results show that the concentration of residual initiator seriously influences the polydispersity index of the resulting polymer. The calculated outcomes of the non-steady state approach are evidently different from those of the quasi-stationary state method when the magnitude of the rate constant of termination is comparable with that of the propagation rate constant, and the difference becomes negligible if the rate constant of the termination (k_t) is much larger than that of propagation (k_p). The polydispersity index of the resulting polymer increases with decreasing ratios of k_t to k_p or M_O to I_O (initial concentrations of monomer and initiator).     

Dynamics of entangled polymer chains with nanoparticle attachment under large amplitude oscillatory shear

This paper presents a nonlinear viscoelastic model for polymer nanocomposites and the computed model response to large amplitude oscillatory shear flow. The model predicts the stress in a mixture of entangled polymer chains, with different convective constraint release (CCR) rates for free chains and nanoparticle‐attached chains, through an averaging scheme which is consistent with double reptation in the Marrucci–Ianniruberto constitutive equation. The nonlinear response of the mixture is evaluated both numerically in terms of Q and by an asymptotic analysis in terms of four frequency dependent parameters of medium amplitude oscillatory shear (MAOS) as well as the intrinsic nonlinearity parameter Q₀ . In the case of free polymer chains alone, the MAOS signatures are comparable to those of the Giesekus model with the notable difference of a minimum in the elastic parameter [e₁] at De >1. The viscous nonlinear parameters of the mixture model depart significantly from those of the free chains, especially in mixtures where the CCR parameter for attached chains is larger than that for the free chains: [v₁] has a prominent minimum and [v₃] has a prominent maximum near De = 2/c, the low frequency plateau region, along with a higher Q₀ compared to the matrix at all Deborah numbers. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 62–76     

Measurement of the orientational elastic constants and the twist viscosity of nematic side chain polymers

Abstract

The temperature dependence of the three elastic constants k _ii (i = 1, 2, 3) and the twist viscosity γ₁ of two nematic side chain polyacrylates and one comparable low molecular weight compound have been measured by means of the Freedericksz effect. The change from the low to the high molecular liquid crystal causes a change of the ratio k ₃₃/k ₁₁ from greater to less than unity, but the order of magnitude of the elastic constants remains the same. In contrast, the twist viscosity of the polymeric liquid crystal is about 1000 times greater in magnitude than that of a comparable low molecular weight liquid crystal. The activation energy for the viscosity of the polymer differs by a factor 3–4 from that of the low molecular weight liquid crystal. The elastic constants as well as the twist viscosity show a quadratic dependence on the order parameter S over a wide temperature range.     

Polymer coupling and theory of on-random crosslinking: an analytical solution

Gel formation is an important feature in free-radical polymer coupling. Due to the different possible combination reactivities of each polymer backbone radical, polymer chains are crosslinked in a non-random manner. Equations of the moments have been derived to predict the pregel molecular weight development and the crosslink density at gel point. This work provides an analytical solution for the differential equations. The model agrees with the Flory-Stockmayer gelation theory under the condition of random crosslinking. The magnitude of deviations from the classical theory for non-random crosslinking depends on the product of the radical termination reactivity ratios (r₁r₂), the ratio of the rate constants of backbone radical generation (k), the ratio of the weight-average chain lengths of primary polymers (y), and the polymer weight fractions (w₂).     

Effect of chain length on rates of diffusion-limited small molecule-polymer and polymer-polymer reactions: Phosphorescence quenching studies

Model interactions have been studied by phosphorescence quenching to obtain a better understanding of the chain length dependence of interpolymeric chain end-chain end reactions such as those involved in the termination step of free radical polymerization. For small molecule-polymer interactions in dilute cyclohexane solution, quenching rate constant (k_q) data agree with the Smoluchowski equation prediction that k_q scales as polymer molecular weight (MW) to the -½ power, confirming self-diffusion control. For polymer-polymer interactions in dilute solution, the chain length dependence is weaker than that predicted by translational diffusion control, as described by the Smoluchowski equation, but is stronger than that predicted by renormalization group theory. For interactions between 70000 MW benzil-end-labeled polystyrene and varying MWs of anthracene-end-labeled polystyrene at 300 g/L polymer, k_q decreases by a factor of 10 in going from MWs of 100 to 1000 g/mol; beyond 1000 g/mol, k_q is nearly independent of chain length. Such effects indicate that the importance of oligomeric radical self-diffusion and polymer radical chain-end segmental mobility must be carefully considered in understanding the termination process in free radical polymerization. © 1996 John Wiley & Sons, Inc.     

Viscoelasticity of a stretched polymer chain with ends exposed to a constant force

The viscoelasticity of a stretched polymer chain with its end particles exposed to oppositely acting forces is studied via collisional molecular dynamics and analytically. A simple model according to which a polymer molecule is a chain of particles linked through freely jointed elastic bonds is adopted. The analytical theory is in good agreement with the results of the computer simulation of time correlation functions in the range of large-scale motions of a polymer molecule. It is found that the decay of correlation functions K _αβμν of fluctuations of the microscopic stress tensor of a chain, K _zzzz, K _zαzα , = K _zαzα , (α = x, y; z is the axis along which the forces act), is slowed down, and their value increases relative to the respective correlation functions of a chain with fixed ends. The greater the force, the higher this difference. The correlation functions that are transverse with respect to the z axis do not differ from those for chains with fixed ends. The results show that, in the calculation of time correlation functions of strongly stretched polymer chains, different statistical ensembles are not equivalent; this must be taken into account in the dynamic theories of heavily deformed polymers.     

Studies towards a tailor-made catalyst for the Diels-Alder reaction using the technique of molecular imprinting

A tailor-made catalytically active polymer catalyzing the bimolecular Diels-Alder reaction is described. Kinetic studies carried out in acetonitrile at 82°C show a 270-fold rate acceleration (k_cat/k_uncat) for the Diels-Alder reaction between tetrachlorothiophene dioxide and maleic anhydride. The imprinted polymer induces Michaelis-Menten kinetics, with an apparent K_m of 42.5 mM and an apparent k_cat of 3.82 × 10⁻² min⁻¹, respectively. Substrate selectivity, accessible binding site analysis, dissociation constant determination, and inhibition study were also performed.     

Oxygen‐binding Protein Fiber and Microgel: Supramolecular Myoglobin–Poly(acrylate) Conjugates

A supramolecular conjugate of myoglobin (Mb) and water‐soluble poly(acrylate), (PA_5k and PA_25k, where 5k and 25k represent the molecular weight of the polymers, respectively), is constructed on the basis of a noncovalent heme‐heme pocket interaction. The modified heme with an amino group linked to the terminus of one of the heme‐propionates is coupled to the side‐chain carboxyl groups of poly(acrylate) activated by N‐hydroxysuccinimide. The ratios of the heme‐modified monomer unit and the unmodified monomer unit (m:n) in the polymer chains of Heme‐PA_5k and Heme‐PA_25k were determined to be 4.5:95.5 and 3.1:96.9, respectively. Subsequent addition of apoMb to the conjugated polymers provides Mb‐connected fibrous nanostructures confirmed by atomic force microscopy. A mixture of the heme‐modified polymer and dimeric apomyoglobin as a cross‐linker forms a microgel in which the reconstituted myoglobin retains its native exogenous ligand binding activity.     

Transamination by Polymeric Enzyme Mimics

Pyridoxamine was linked to a series of polyethylenimines (PEIs) with M_n=600, 1800, 10,000, and 60,000, both simply permethylated and with additional attached dodecyl chains. They were examined in the transamination of pyruvic acid and of phenylpyruvic acid, and showed Michaelis? Menten behavior. The values of k₂ and of K_M determined showed only small variations with polymer size. Thus, the previously reported strong advantage of pyridoxamines attached to the M_n=60,000 PEI, relative to simple pyridoxamine alone, is seen to almost the same extent with the smaller PEIs.     

A comparison of the absolute reactivity of vinyl monomers. I. Kinetic studies on radical polymerization of vinyl monomers initiated by a Mn3+–diglycolic acid redox system

The kinetics of polymerization of acrylamide (AM), acrylic acid (AA), and acrylonitrile (AN) initiated by the redox system Mn³⁺–diglycolic acid (DGA) was studied. All three systems followed the same mechanism; namely, initiation by an organic free radical arising from the oxidation of diglycolic acid and termination by the interaction of polymer radicals with Mn³⁺ ion. The rate coefficients k_i/k₀ and k_p/k_t were related to monomer and polymer radical reactivity, respectively. An inverse relation between monomer and polymer radical reactivity was observed. Monomers with higher Q values gave higher k_i/k₀ values but lower k_p/k_t values. The e values of the monomers were important in determining the reactivities of monomers with nearly the same Q values.     

Rheological Behavior of Dope Solutions of Poly(acrylonitrile‐co‐itaconic acid) in N,N‐dimethylformamide: Effect of Polymer Molar Mass

The rheological behavior of dope solutions of poly(acrylonitrile‐co‐itaconic acid) or poly(AN‐co‐IA) is important from the point of view of deriving the spinning conditions for good quality special acrylic fibers. The viscosity of the resin dope is dictated by the polymer concentration, molar mass, temperature and shear force. The dynamic shear rheology of concentrated poly(AN‐co‐IA) polymer dope solutions in N, N‐dimethylformamide, in the molar mass (M¯_v) range of 1×10⁵ to 1×10⁶ g/mol, was investigated in the shear rate (γ′) range of 1×10¹ to 5×10⁴ min^?1. An empirical relation between η and M¯_v was found to exist at constant shear rate. The dope viscosity was dependent on the molar mass and the shear rate at a given temperature (T) and concentration. The polymer molar mass index of dope viscosity (m) was calculated as functions of concentration (c), shear rate and temperature. The m values increased with shear rate and temperature. A master equation relating m, with shear rate and temperature was derived for a given dope concentration. At higher shear rates, m tends to the value of 3.4, which is close to the molar mass index of viscosity reported for molten thermoplastics. m increased significantly with shear rate and nominally with temperature, while an increase in concentration decreased it. The onset of shear thinning of the dope shifted to a lower shear rate regime with an increase in polymer concentration and the molar mass. For a given value of molar mass, the increase in viscosity of the dope solution with polymer concentration was dependent on the shear rate.     

Linear shear viscoelasticity of confined,end-attached polymers in a near-theta solvent

Diblock copolymers of polystyrene and polyvinylpyridine, end-attached to mica by the traditional method of selecting one block to be insoluble and the other block to be soluble in the solvent, were studied with surface-force experiments while immersed in trans-decalin, a near-theta solvent for the polystyrene block, with special attention given to the small-amplitude shear viscoelastic response. The relaxation time, defined as the inverse frequency at which the effective loss modulus equaled the effective storage modulus, was studied not only as a function of the film thickness but also as a function of the grafting density. The relaxation times started to slow in direct proportion to diminishing surface separation when the surface separation took the value D ≈ L_o/3 (where L_o is the thickness of the uncompressed end-attached layer). Attempts to make comparisons with available theories met with limited success. To test experimentally the origin of this shear viscoelastic slowdown, similar measurements were made with adsorbed polystyrene with a molecular weight similar to that of the polystyrene moiety of the diblock copolymer, and it was found that high magnitudes of the effective viscoelastic shear moduli appeared only when the compression was much larger. In a control experiment in which interpenetration between opposed end-attached chains was precluded, we also studied the case of adsorbed polystyrene–polyvinylpyridine on one side and a bare mica surface on the other side, and the effective viscoelastic shear forces were reduced by nearly 1 order of magnitude. By inference, in the opposed diblock copolymer systems, we attributed the slowdown of the relaxation times with decreasing film thickness to the interpenetration of end-attached chains. Additional comments are made regarding the ratio of shear forces to compressive forces, which is called the small-strain friction coefficient. This is believed to be the first quantification of the linear-response relaxation time of end-attached polymer layers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3487–3496, 2005