Intrinsic viscosity in branched free-radical polymers

The intrinsic viscosity ratio [η]_B/[η]_L was calculated as a function of average branching density for trifunctionally branched, free-radical polymers. Calculations were made for the g^1/2, g^3/2, and h³ rules, using realistic distributions of molecular weights and branches. Experimental data on branched poly(vinyl acetate) lay between the curves obtained from the g^1/2 and h³ relations.     

Flow properties of branched polydisperse polymers

Viscosity and normal-stress difference as functions of shear rate were examined for poly(vinyl acetate) samples with various degrees of random branching in diethyl phthalate solution. At moderate concentration (c = 0.17 g/ml) the viscosities were depressed by branching, in fair accord with the Bueche theory. However, at higher concentrations (c = 0.35 g/ml) the data showed a progressive trend in the direction of viscosity enhancement by branching, a characteristic which has been observed by other workers in undiluted branched polymers. Accompanying viscosity enhancement was an increase in the temperature coefficient of viscosity, an increase in recoverable compliance (estimated from steady-state normal-stress data) and an early onset in the shear rate dependence of viscosity.     

Viscosity and normal stresses in branched polydisperse polymers

The steady-flow behavior of five samples of branched poly(vinyl acetate) has been studied with the Weissenberg rheogoniometer. The branching densities and molecular weight distributions were known from an analysis of the polymerization kinetics. Measurements were made on concentrated diethyl phthalate solutions (0.170 and 0.225 g/ml) at temperatures of 30 and 70°C. The viscosities of all solutions at zero shear rate were less than of solutions of linear poly(vinyl acetate) with the same weight-average molecular weight. The amount of decrease was in excellent agreement with Bueche's theory of melt viscosity in branched systems. The viscosity versus shear rate curves were surprisingly independent of molecular weight distribution, the data from all samples being superimposable on the same master curve. Relaxation times derived independently from the viscosity behavior and the normal stress data were of similar magnitude and always close to the Rouse relaxation time of each solution.     

Intrinsic viscosity of flexible ring polymers

The intrinsic viscosity of flexible ring polymers with a finite number of segments is computed with both exact and approximate eigenvalues λk, in the frame of the elastic necklace model. It is shown that exact and approximate calculations of the Flory constant and the Kuhn-Mark-Houwink exponent of the non-free-draining limit are compatible with h^* ? 0.25 and N ≥ 100.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.     

On rheological properties of polydisperse polymers

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: $\text{η}{}_0\text{～}\text{M}{}^{\mathrm{\alpha }}{}_{\mathrm{<mtext>w</mtext>}}$; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: , and in the general case α₁ ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

Analytical theory of ideal polydisperse polymers at interfaces

We use a recently developed continuum theory to present an exact treatment of the interfacial properties of ideal polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. We apply our theory to a number of cases, including, non-adsorbing and adsorbing surfaces, as well as telechelic chains.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Synthesis of new branched urethane-triazole polymers

An AB₂ monomer obtained via the reaction of hexamethylene diisocyanate with 1,3-diazidopropan-2-ol and 2-propyn-1-ol contains one triple bond (A) and two azide groups (B₂). Hyperbranched urethane-triazole polymers were synthesized through stepwise polymerization of this monomer via 1,3-dipolar cycloaddition. Owing to the presence of impurities of compounds with four azide groups (the products of the reaction of hexamethylene diisocyanate with two molecules of diazidopropanol) and two propyne groups (the product of the reaction of hexamethylene diisocyanate with two molecules of 2-propyne-1-ol) in the aforementioned monomer, uretane-triazole “polymers” are not classical huperbranched polymers, they are highly branched polymers that are soluble in aprotic polar solvents and have weight-average molecular masses of 5–260 and values of the exponent in the Kuhn-Mark-Houwink equation of 0.23–0.36.     

Amphiphilic branched polymers as antimicrobial agents

Cationic amphiphilic polymers were prepared from PEI and functional ethylene carbonates bearing cationic, hydrophobic or amphiphilic groups. The polymers are designed to exhibit antimicrobial properties. In a one-step addition, different functional ethylene carbonates were added to react with the primary amine groups of PEI. The water soluble polymers were studied regarding their ability to form soluble aggregates. Their hydrodynamic radii, their inhibition potential against proliferation of E. coli and their hemolytic potential were determined. A structure-property relationship was established by analyzing the antimicrobial activity as a function of the ratio of alkyl to cationic groups, length of the alkyl chains, and molecular weight of the PEI.     

Molecular weight distribution in branched polymers

The distribution of molecular weights in realistic free-radical polymerizations with branching was analyzed theoretically. Series solutions were obtained for the fraction of molecules with r repeating units and the number of branch points contained in molecules with r repeating units. Branching by transfer processes was found to increase the proportion of both high and low molecular weight components in the system. The apportioning of branch points among r-mer molecules was shown to be somewhat narrower than a Poisson distribution. The major difference between the calculated distributions and previous model distributions for branched systems was the absence of discontinuities in the moments at all levels of branching.     

Intrinsic viscosity of polyelectrolytes in salt solutions

The dependence of the intrinsic viscosity of polyelectrolytes on the concentration of added salt is given satisfactorily by a formula obtained recently. A new viscosity—molecular weight relation gives satisfactory agreement with experiments.     

Intrinsic viscosity of polystyrene in mixed solvents

The intrinsic viscosity of a single sample of polystyrene was measured as a function of the composition of solvent in three mixed solvent pairs. The parameter Y introduced by Shultz and Flory was useful for prediction of trends, but severely overestimated the effect of solvent (1)–solvent (2) interaction on the expansion of polymer coils. The system polystyrene–cyclohexane–ethyl acetate was studied in detail for five samples of polystyrene. The analysis of the data provided strong experimental proof of a strict validity of the Mark–Houwink–Sakurada relation. The dependence of the Mark–Houwink–Sakurada exponent α on the composition of the solvent mixture was unexpectedly unsymmetrical. The unperturbed dimentions of the polystyrene chain are reduced by specific interaction of polystyrene with carbonyl groups in the solvent mixture.     

Size exclusion chromatography of branched polymers: Star and comb polymers

Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight‐average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb‐branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD.