The effect of inertia on the intrinsic viscosity of polymers

For the model of an elastic dumbbell, i.e., two beads connected by a Hookean spring, the Langevin equations for the beads are formulated. It is taken into account that the friction force contains terms resulting from the inertia of the liquid. The contribution of the dumbbell to the viscosity is calculated from the rate of energy dissipation. When the inertia of the liquid is neglected, the viscosity contribution reduces to Kramers' result and is independent of the mass of the beads. When the inertia terms are added, the result is nearly independent of this mass, but shows a dependence on the density of the liquid. In liquids of low viscosity, the extra term resulting from the inertia may be as large as 25% of the total viscosity contribution.     

Comments on the theories of the intrinsic viscosity of chain polymers

The theory of intrinsic viscosity developed recently by the present author is examined and compared with experiments and the theories by Peterlin, Kirkwood and Riseman, Brinkman, and Debye and Bueche. The fundamental assumptions and essential approximations in the theories are criticized.     

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight‐average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2009–2018, 2000     

Correlation between glass transition temperature and chain structure for randomly crosslinked high polymers

The empirical form for the dependence, T_g(n) ≅ T_g(∞)·(1 + α/n), of the glass transition temperature T_g on the average number n of repeat units between crosslinks, is generalized for randomly crosslinked high polymers. The new form, T_g(n) ≅ T_g(∞) · [1 + c/(n·N_rot)], is based on a correlation study of data for 77 samples of 10 different sets of resins. The fitting parameter α is resolved into composition-dependent N_rot and composition-independent c terms. N_rot summarizes the average number of rotational degrees of freedom per repeat unit, and is estimated in a straightforward manner from the structure and mol fraction of each repeat unit. The value of c is found from data analysis to be 5 ± 2. The results of this work are consistent with expectations based on the entropy theory of glasses, and provide improved understanding and predictive ability for the properties of crosslinked polymers. © 1996 John Wiley & Sons, Inc.     

Molecular weight distributions of linear polymers: Detailed analysis from GPC data

The GPC method is used widely to measure molecular weights of linear polymers. High-quality GPC data contains detailed information on many aspects of the polymer's molecular weight distribution (MWD). This information can be extracted from the data using computer analysis. Equations have been derived for the two simplest MWD functions in the GPC coordinates: the Flory function (one growing polymer chain produces one polymer molecule), and for the case when two polymer radicals combine into one polymer molecule. The equations were used to analyze MWD of two classes of polymers. The first class includes polymers with narrow MWD: polyethylene, ethylene-propylene and ethylene-hexene copolymers, syndiotactic polystyrene, and radical polystyrene. The second class includes polymers with broad MWD: ethylene copolymers and polypropylene produced with heterogeneous, Ti-based catalysts. The examples demonstrate that the resolution of complex GPC curves into their constitutents serve as an important source of information about kinetics of polymerization reactions. © 1995 John Wiley & Sons, Inc.     

Relation between preferential solvation and intrinsic viscosity of polymers in solvent mixtures

Preferential solvation and intrinsic viscosity measurements are reported for three systems: polystyrene + benzene + methanol, polystyrene + carbon tetrachloride + methanol, and poly(2-vinylpyridine) + ethanol + cyclohexane. Plots of the coefficient of preferential solvation λ′ as a function of variation of the segment density Δ_ρ for a given ternary system, give a single curve for a large range of molecular weight and solvent mixture composition. This correlation between λ′ and Δ_ρ is verified in previously published data.     

Elasticity and structure of crosslinked polymers

Summary The subject of this work is to determine the dynamic and static elastic properties of polymer networks and to compare the experimental results with theoretical predictions.It is found that poly(dimethylsiloxane) (PDMS) networks on the one hand and polyisoprene (IR) and natural rubber (NR) networks on the other hand show different behaviour in frequency dependence of the storage modulusG is observed in the range 10^–3 – 1 Hz, contrary to IR or NR. The reason for this is the absence of entanglements in PDMS.Comparing the measured static moduli with those calculated by rubber elasticity theory, we found that the front factorA· <r ²>/<r ²>₀ is near to 0.5 in case of PDMS, but near to I for IR/NR networks. Both parts of the front factor may possibly cause this difference. As the PDMS chains possess a relatively high mobility we can assume that fluctuations of the junction points are less restricted than in IR/NR. This causes a structure factor A smaller than 1 in agreement with Flory's recent theory.According to James and Guth, the network chains tend to contract during the crosslinking process. This will be more likely in the networks of entanglement-free, highly mobile PDMS chains than in IR or NR rubbers. Hence the memory term <r ²>/<r ²>₀ is smaller for PDMS than for IR/NR.Both alternative explanations are based on the different mobility of the chains considered. It may be assumed that the front factor is influenced by both effects and not only by the fluctuations of crosslinks.Dedicated to Professor Dr. K. Ueberreiter on his 70th birthday     

High-resolution NMR of crosslinked polymers: Effects of crosslinked density and solvent interaction

Measurements have been made of the dependence of nuclear magnetic resonance bandwidths of polymers on the degree of crosslinking. Poly(methyl methacrylates) and poly(hexadecyl acrylates) were studied. Three regions of behavior are apparent: (1) in lightly crosslinked materials, bandwidths are quite insensitive to the degree of crosslinking, and the networks behave almost as linear polymers in solution; (2) in moderately crosslinked material, bandwidths are significantly affected by the degree of crosslinking; and (3) in highly crosslinked materials, bandwidths are extremely sensitive to crosslink density, and the polymer peaks become so broad that they disappear almost completely. These results indicate that segmental motion of a polymer in solution is not a function solely of its molecular weight, and that a certain degree of crosslinking is required to restrict polymer motion at the segmental level. The solvent (benzene) peak is always a singlet in swollen poly(methyl methacrylate) systems with swelling ratios up to 6.4 (regions 1 and 2, above) but as the swelling ratio further decreases to 3.5 (region 3), the solvent peak splits into a doublet; this phenomenon may indicate the existence of two different arrangements of solvent molecules in the swollen network, for which interchange is not sufficiently rapid to produce a single line.     

Exploring the domain validity of the equations relating the intrinsic viscosity to the molecular weight by using the characteristic numbers of polymers

Plotting log[η] versus logM (Mark-Houwink-Sakurada equation) we observe a crossover region in which a continuous variation of the exponent of this equation takes place. This crossover region is delimited by two characteristic numbers: Nc (or Mc), the number of statistical segments (or the molecular weight) in the onset of excluded volume behavior and Nc' (or Mc') the number of statistical segments (or the molecular weight) in the onset of the complete excluded volume behavior. Relations are given in order to obtain these numbers. The Stockmayer-Fixman-Burchard equation is valid for the flexible and wormlike polymers in the molecular weight region which lies above the crossover region while the Dondos-Benoit equation is valid in the medium and low-molecular-weight region including the crossover region.     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

The interaction parameter of crosslinked networks and star polymers

Recent results on blends containing star polymers have revived the interest on the interaction parameters of structures that contain junctions between chains, a matter which can be connected with the earlier studies on the influence of crosslinks on the interaction parameters of polymer networks and gels. Here, we review results on crosslinked networks and star polymer solutions together with the more recent work on star polymer blends. The review covers swelling and elastic deformation of gels, differential vapour sorption between crosslinked and uncrosslinked polymers, osmotic equilibrium of gels and of star polymer solutions, and neutron scattering of polymer blends containing star polymers. In the systems reviewed, the interaction parameters of stars and networks differ from those of linear chains, and the difference is attributed mainly to entropic effects.     

Synthesis and rheology of methacrylic acid-ethyl acrylate crosslinked polymers

The rheological behaviour of methacrylic acid-ethyl acrylate copolymers (MAA 61.9–78.5 mol%) and terpolymers with two crosslinking agents, i.e. ethylene glycol dimethacrylate (EGDM, 0.23–4.83 mol%) or N, N′-methylene bisacrylamide (MBAM, 0.29–1.48 mol%) has been studied. The effect of pH, shear rate, solid content of the solution, and the addition of electrolyte on the viscosity has been reported. As the viscosity is a function of neutralization of carboxylic acid groups, it was found to be highly dependent on pH. Addition of electrolytes (0.5–1.5%) led to a drastic drop in the viscosity. The influence of different crosslinking agents on the viscosity was also studied and N, N′-methylene bisacrylamide was found to be more efficient than ethylene glycol dimethacrylate. The gel content of the crosslinked polymers was determined to obtain an idea of the degree of crosslinking of the polymers.     

Effect of temperature on the intrinsic viscosity and conformation of different pectins

The effects of temperature on the intrinsic viscosity and on the conformation of pectin obtained from Citrus, Apple and Sunflower in a 0.17M NaCl solution were studied. Mark-Houwink plots for Orange, Apple and Sunflower pectin were obtained using HPSEC with online light scattering and viscosity detection. The intrinsic viscosity and flow activation energy E _a of pectin from the sources studied were measured over the temperature range 20–60°C. E _a values were 0.67, 0.69, 1.34, and 1.44 × 10⁷ J/(kmol) for commercial Citrus, Orange, Sunflower and Apple pectin, respectively. Intrinsic viscosity decreased linearly with increasing temperature, for all pectins except Apple one. These results clearly indicated that Apple pectin underwent structural changes that were more drastic than those that occurred for pectin from the other sources. E _a increased with decreasing weight average molar mass M _w indicating that pectin with low M _w were more asymmetric than pectin with higher values of M _w. Changes in the Huggins coefficients K _h with temperature for pectin from the various sources were attributed to the ability of pectin to aggregate, disaggregate and re-aggregate according to the temperature at which it was stored.