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).     

Isothermal crosslinking studies on polyquinoxalines by dynamic mechanical methods

Torsional braid analysis was used to investigate the crosslinking behavior of linear quinoxaline polymers with and without reactive side groups. The kinetic parameter followed was the glass transition temperature during isothermal exposure in an inert atmosphere. With high molecular weight polyamide-quinoxaline copolymers (PPAQ), an initial decrease in T_g was observed during heat exposure which was followed by a subsequent increase in T_g. This was attributed to simultaneous chain scission and crosslinking reactions. Since the effect of random chain scission on the initial change in T_g of the highest molecular weight polymer samples is much stronger than on low molecular weight analogues, a T_g minimum was observed only on the highest molecular weight polymers. Because of the complexity of the reactions occurring one must consider the activation energies obtained from the Arrhenius plots as “apparent” activation energies. No attempt was made to elucidate the mechanisms of these reactions. It has been shown that isothermal heat exposure of high-temperature aromatic polymers in an inert atmosphere leads to crosslinking. In general, however, linear polymers that have reactive side groups such as methyl or carboxyphenyl groups along the polymer chain crosslink more rapidly than the analogs without these groups.     

Evaluation of the polymer-solvent interaction parameter χ for the system cured styrene butadiene rubber and toluene

One of the most popular cured rubbers used in industrial applications is styrene butadiene rubber (SBR) and frequently its network structure is studied by means of swelling techniques in solvent. Normally, toluene is used as solvent in this test. In order to estimate the crosslink density from the equilibrium volume fraction of rubber in the swollen state, the correct evaluation of the Flory-Huggins interaction parameter χ is necessary. This work covers the swelling behavior of cured SBR in toluene. The rubber was vulcanized with different amounts sulfur and accelerator at 433 K in order to obtain several network structures and crosslink densities. Network characterisations of the compounds were made by swelling measurements in the frame of the Flory-Rehner relationship using the molecular weight of the network chain between chemical crosslinks obtained previously by mechanical tests. A relationship between χ and v_r, the polymer volume fraction at equilibrium (maximum) degree of swelling, was established for the cured SBR/toluene system. It was found that χ is not a constant but depends on the crosslink density in the sample. The types of crosslinks in these samples where estimated applying this function to the swelling behavior of the compounds previously treated with the thiol probe method.     

Formation of linear polymers in confined intranetwork space during synthesis of sequential semi-interpenetrating polymer networks

Sequential semi-interpenetrating polymer networks based on polyurethanes with different crosslink densities and linear polystyrene, poly(butyl methacrylate), and poly(methacrylic acid) have been studied. For the parent polyurethanes, the molecular mass of chain segments between crosslink junctions is estimated by the Flory-Rehner method. The kinetics of formation of linear polymers in semi-interpenetrating polymer networks is investigated as a function of the crosslink density of the polyurethane network. The molecular-mass distributions of linear polymers developed in semi-interpenetrating polymer networks are examined by size-exclusion chromatography. The relationship between the kinetics of formation of linear components under the conditions of confined space and their molecular mass is established.     

Determination of the degree of swelling and crosslinking of extremely small polymer gel quantities by analytical ultracentrifugation

The degree of crosslinking of very small amounts of polymer gel, encountered in the characterization of the molecular structure of rubber polymers or of polymers in powder form, cannot be determined satisfactorily by measurement of elasticity or conventional swelling. Therefore a method has been developed which enables us to determine the degree of crosslinking of such polymer systems reliably. This method is based on the measurement of equilibrium swelling by sedimentation in the analytical ultracentrifuge. The degree of swelling can either be used directly as a relative measure of the average degree of crosslinking or as basis for calculating the average degree of polymerization of the molecule chains between two crosslink sites according to the theory of Flory and Rehner. The efficiency of the method is demonstrated by several examples of application (differently crosslinked polybutadienes, gel portions of various polychloroprenes and polyurethane foams).Dedicated to Dr. Gerhard Fritz on the occasion of his 60th birthday.     

Swelling and Network Parameters of 1-Hexadecene-Co-Trimethylolpropane Distearate Monoacrylate Sorbers

Linear and crosslinked copolymers with different compositions of 1-hexadecene and trimethylolpropane distearate monoacrylate monomers were synthesized and evaluated for oil-absorbency application. Different concentrations of ethylene glycol diacrylate (EGDA) and ethylene glycol dimethacrylate (EGDMA) crosslinkers were used. The concentration of both crosslinkers was varied from 0.5% to 2%. Copolymer compositions were determined from ¹H NMR spectroscopy. Monomer reactivity ratios were calculated using Fineman-Ross and Kelen-Tudos techniques at low conversions. The oil absorbency and swelling rate constant were measured and influenced mainly by the degree of crosslinking and the hydrophobicity of copolymer units. The final equilibrium oil content, volume fraction of polymer and swelling capacity were determined at 298 K. The effective crosslinking density V_e, theoretical crosslink density V_t, the average molecular weight between the crosslinks M_c and the polymer-toluene interaction parameter χ were determined from swelling measurements. The efficiencies of EGDA and EGDMA crosslinking agents toward copolymers were determined.     

Investigation of molecular motions of crosslinked polyepichlorohydrin by nuclear magnetic resonance spectroscopy

The molecular motion of crosslinked polyepichlorohydrin (PECH) is studied qualitatively by NMR techniques. The results of temperature dependence of ¹H T₂ and T₁ indicate that the crosslinking (crosslink density < 3%) restricts molecular motions of the polymer even far above its T_g. The ¹H T₁ minimum, corresponding to the large-scale chain-motion of crosslinked PECH, shifts to higher temperatures with increasing crosslink density. ¹H T₂ data also show that the crosslinking hinders free chain motions of the polymer above its T_g. The ¹³C T₁ relaxation time is sensitive to such motional changes as well. ¹³C linewidths of crosslinked PECHs vary with the crosslink density in both the swollen state and the solid state. The mechanism of ¹³C linewidth broadening of crosslinked polymers is discussed in detail. In the case of PECH, the linewidth broadening is caused by changing molecular environment due to crosslinking (such as presence of various chemical shift structures and freezing effects in conformational environment as chain mobility decreases), rather than increasing correlation times, which shorten the relaxation time (T₂) of polymer chains. © 1994 John Wiley & Sons, Inc.     

Novel amphiphilic network polymers consisting of nonpolar,short primary polymer chains and polar,long crosslink units: Influence of characteristic dangling chains on swelling behavior of resulting amphiphilic gels

Novel amphiphilic network polymers consisting of nonpolar, short primary polymer chains and polar, long crosslink units were prepared, and the swelling behavior of resulting amphiphilic gels is discussed by focusing on the influence of characteristic dangling chains; that is, benzyl methacrylate (BzMA) was copolymerized with tricosaethylene glycol dimethacrylate [CH₂?C(CH₃)CO(OCH₂CH₂)₂₃OCOC(CH₃)?CH₂, PEGDMA‐23] in the presence of lauryl mercaptan as a chain‐transfer agent because BzMA forms nonpolar, short primary polymer chains and PEGDMA‐23 as a crosslinker contains a polar, long poly(oxyethylene) unit. The enhanced incorporation of dangling chains into the network polymer was brought by shortening the primary polymer chain length, and copolymerization with methoxytricosaethylene glycol methacrylate, a mono‐ene counterpart of PEGDMA‐23, enforced the incorporation of flexible dangling poly(oxyethylene) chains into the network polymer, although the former dangling chains as terminal parts of primary poly(BzMA) chains were rather rigid. Then, the influence of characteristic dangling chains on the swelling behavior of amphiphilic gels was examined in mixed solvents consisting of nonpolar t‐butylbenzene and polar methanol. The profiles of the solvent‐component dependencies of the swelling ratios were characteristic of amphiphilic gels. The introduction of dangling poly(oxyethylene) chains led not only to an increased swelling ratio but also to sharpened swelling behavior of amphiphilic gels. The swelling response of amphiphilic gels was checked by changing the external solvent polarity. The dangling chains with freely mobile end segments influenced the swelling response of gels. The amphiphilic gels with less entangled, collapsed crosslink units exhibited faster swelling response than the ones with more entangled, collapsed primary polymer chains. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2192–2201, 2004     

The kinetics of poly(N-isopropylacrylamide) microgel latex formation

Conversion versus time curves were measured for poly(N-isopropylacrylamide) microgel latexes prepared by polymerization in water with sodium dodecyl sulfate, SDS. Polymerization rates increased with temperature with methylenebisacrylamide crosslinking monomer consumed faster thanN-isopropylacrylamide. The particle diameter decreased with increasing concentrations of SDS in the polymerization recipe and there was evidence that the rate of polymerization increased somewhat with SDS concentration. Particle formation occurred by homogeneous nucleation as micelles were absent.Comparison of particle size distributions from dynamic light scattering to those from a centrifugal sizer led to the conclusion that larger particles within a specific latex were less swollen with acetonitrile than were the smaller ones. This was interpreted as evidence for the polymer in larger particles having a higher crosslink density. Particle swelling was estimated from swelling ratios defined as the particle volume at 25 °C divided by the volume at 50 °C. In the absence of crosslinking poly(N-isopropylacrylamide) linear chains would disolve at 25 °C. The swelling results indicated that the average crosslink density in the particles decreased with conversion. This was explained by the observation that the methylenebisacrylamide was consumed more quickly and is typical of crosslinking in emulsion polymerization where polymer particles have high polymer concentrations at their birth.     

Sorption and swelling in ultra-thin polymer films

Different polymers were investigated with respect to the sorption of solvents and gases. Depending on the chemical nature of the polymers this sorption leads to polymer swelling. The degree of swelling D/D₀ was measured utilizing Small angle X-ray scattering (SAXS) as well as Surface plasmon resonance (SPR). From the change in film thickness after swelling in different solvents Hildebrand parameters of the polymers were determined. By crosslinking of the polymer films the degree of swelling can be controlled. In the case of ultra-thin polyimide films a higher degree of crosslinking led to a decreased selectivity of the transport of gases through the membrane. Reptation of macromolecules was also investigated and the influence of polymer swelling in different solvents has a great influence on the selectivity and diffusion coefficient.     

Determination of the radiation yield of hydrogels crosslinking

The ability of polymer to crosslink or exposure to radiation is frequently represented by a G value, the number of crosslinks per 100 eV absorbed. Several methods are available for its determination, the most frequent being the dose D_g required to form an incipient network since (with many systems) this corresponds to one crosslinked unit per weight average molecular (δ = 1). Its determination therefore depends on a knowledge of the molecular weight of the starting polymer. An alternative method, far less frequently used, is to measure the degree of swelling of a crosslinked network. This involves a knowledge of the Flory-Huggins interaction parameter μ and of the initial number average M_n(0). However if the concentration V_e of effective chains (deduced from swelling) is plotted against dose D, the slope gives G(X) directly, independent of M_n(0). This applies only when the system is very largely crosslinked. It may also be used to determine G(X) even when starting from the monomer itself (i.e. combining polymerization and crosslinking). It is shown that, for a series of polymers, irradiated either as liquids or in solution, the theoretical relation between swelling and crosslink density is followed, and the G(X) values derived from swelling compare well with those given in the literature, and based on gel fraction.     

Quantification of radiation induced crosslinking in a commercial, toughened silicone rubber, TR55 by H MQ-NMR

Radiation induced degradation in a commercial, filled silicone composite has been studied by SPME/GC-MS, DMA, DSC, swelling, and multiple quantum NMR. Analysis of volatile and semi-volatile species indicates degradation via decomposition of the peroxide curing catalyst and radiation induced backbiting reactions. DMA, swelling, and spin-echo NMR analysis indicate an increase in crosslink density of near 100% upon exposure to a cumulative dose of 250 kGray. Analysis of the sol fraction via Charlesby-Pinner analysis indicates a ratio of chain scission to crosslinking yields of 0.38, consistent with the dominance of the crosslinking observed by DMA, swelling and spin-echo NMR and the chain scissioning reactions observed by MS analysis. Multiple quantum NMR has revealed a bimodal distribution of residual dipolar couplings near 1 krad/s and 5 krad/s in an approximately 90:10 ratio, consistent with bulk network chains and chains associated with the filler surface. Upon exposure to radiation, the mean 〈Ω_d〉 for both domains and the width of both domains increased. The MQ-NMR analysis provided increased insight into the effects of ionizing radiation on the network structure of silicone polymers.     

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.     

Reentrant phase transition and network parameters of hydrophobically modified poly[2-(diethylamino)ethylmethacrylate-co-N-vinyl-2-pyrrolidone/octadecyl acrylate] hydrogels

Hydrophobically modified poly[2-(diethylamino)ethylmethacrylate-co-N-vinyl-2-pyrrolidone/octadecyl acrylate] [P(DEAEMA-NVP/OA)] hydrogels with different OA content were prepared by free-radical crosslinking copolymerization of corresponding monomers in tert-butanol. The swelling equilibrium of the hydrogels was investigated as a function of temperature and hydrophobic comonomer content in pure water. An interesting feature of the swelling behavior of the P(DEAEMA-NVP/OA) hydrogels was the reentrant phase transition where the hydrogels collapse once and reswell as temperature increased. The average molecular mass between crosslinks and polymer-solvent interaction parameter (χ) of the hydrogels were calculated from equilibrium swelling values. The enthalpy (ΔH) and entropy (ΔS) changes appearing in the χ parameter for the hydrogels were determined by using the Flory-Rehner theory. It was observed that the experimental swelling data of the hydrophobic hydrogels at different temperature agreed with the Flory-Rehner theory, that provided that the sensitive dependence of χ parameter on both temperature and polymer concentration is taken into account.     

Characterization of resulting network polymer precursors in stepwise crosslinking diepoxide/diamine polymerization

Our previous mechanistic discussion of network formation in chainwise crosslinking multiallyl polymerization was extended to stepwise crosslinking diepoxide/diamine polymerization, typically including bisphenol‐A diglycidyl ether (BADGE) and 4,4′‐diaminodiphenylmethane (DDM). In allyl polymerization a monomer chain transfer is an essential termination reaction, providing only oligomeric primary polymer chains. Therefore, crosslinking multiallyl polymerization could be in the category of a classical gelation theory. Thus, the gelation behavior was discussed by comparing the actual gel point with the theoretical one. Then the resulting network polymer precursors (NPPs) were characterized by size‐exclusion chromatography‐multiangle laser light scattering‐viscometry to clarify the stepwise crosslinking BADGE/DDM polymerization mechanism. Notably, the intrinsic viscosity ratio [η]_NPP/[η]_Linear tended to decrease with the progress of crosslinking and finally, it reached less than 0.2. This suggests that the structure of resulting NPP becomes dendritic at a conversion close to the gel point. These dendritic NPPs can collide with each other to form crosslinks between NPPs, eventually leading to gelation as a reflection of the high concentration of NPP. The dilution effect on gelation was marked in polar solvent; no gelation was observed at a dilution of 1/5. However, in nonpolar solvent the gelation was promoted by dilution; this is ascribed to enhanced crosslink formation between NPPs through hydrogen bonding due to abundant hydroxyl groups in the NPP generated by the polyaddition reaction. Finally, the subject of “Is cured epoxy resin inhomogeneous?” is briefly discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Peroxide-initiated crosslinking of maleic anhydride-modified low-molecular-weight polybutadiene. II. Crosslinking degree and thermal degradation of cured polymers

The crosslinking density and thermal properties of peroxide-crosslinked low-molecular-weight polybutadiene and its modification products with maleic anhydride were studied. It was shown that the Flory-Rehner equation may be used for describing the equilibrium swelling of the studied systems. The molecular weight between crosslinks calculated from this equation has values from 117 to 216. It was found thermogravimetrically that the thermal stability of modified polybutadiene is lower than the unmodified material. The thermal destruction of the polymers studied is a step-by-step reaction, the first being of zero order, with activation energy of 76.6–112.6 kJ/mole, the second, a first-order reaction with an E_a of 286.8–363.4 kJ/mole.     

Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks

The theory of rubber elasticity relates the elastic modulus of unfilled amorphous rubber to the concentration of elastically effective strands. A theoretical relation between this concentration and the concentrations of potential entanglements, random tetrafunctional crosslinks, and chain ends was proposed recently. In the present work, the new relation was combined with the theory of rubber elasticity and verified experimentally. Polydimethylsiloxane samples were cured by ⁶⁰Co irradiation and were extensively extracted to determine gel fraction, which was used to calculate concentrations of crosslinking and scission due to irradiation. Equilibrium modulus values determined from creep tests were in excellent agreement with those calculated using the new relation if the average spacing between potential entanglements is 116 (CH₃)₂SiO units. Thus, in typical commercial silicone rubbers, the contribution to the modulus from trapped entanglements is greater than the direct contribution from crosslinks. The new relation allows the calculation of crosslink concentrations from modulus measurements on other unfilled rubbers once the potential entanglement spacing of the polymer is determined.     

Postgel properties in the statistical crosslinking of heterochains. I. Systems with N types of chains

The heterochain crosslinking model describes nonrandom crosslinking of polymer chains and is an extension of the classical Flory/Stockmayer gelation theory. We consider the postgelation relationship for the system consisting of N types of polymer chains, in which the probability that a crosslink point on an i‐type chain is connected to a j‐type chain is explicitly given by p_ij. The analytical solutions for the weight fraction of the sol, the number‐average and weight‐average molecular weights within the sol fraction, and the crosslinking density within the sol and gel fractions are derived for the systems, with each type of chain conforming to the Schulz–Zimm distribution. Illustrative calculations are shown for the systems consisting of two and three types of chains, and the obtained results agree with those from the Monte Carlo method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2333–2341, 2000     

A thermodynamic study of the crosslinking of methyl silicone rubber

The crosslinking reaction in a two component methyl silicone rubber has been studied by thermomechanical analysis (TMA) and differential scanning calorimetry (DSC). The rubber was formed from two methyl silicone prepolymers; one containing reactive hydrogens every 50 to 100 groups and the other polymer containing pendant vinyl groups at the same frequency. In the presence of a platinum catalyst above 60°C crosslinking proceeds without a loss or gain in weight. The heat of reaction, energy of activation (calculated by two methods) crosslink density and elastic modulus (Young's) were studied as a function of prepolymer concentration, dilution and swelling. A preliminary value for the heat of reaction per mole of SiH and SiCHCH₂ has been calculated. From crosslink density measurements both by hexane swelling and TMA and DSC heats of reaction a qualitative picture has been obtained of the role of entangled chains in producing effective crosslinks.     

ENHANCED WATER SORPTION OF A SEMI-INTERPENETRATING POLYMER NETWORK (IPN) OF POLY(2-HYDROXYETHYL METHACRYLATE) (PHEMA) AND POLY(ETHYLENE GLYCOL) (PEG)

ABSTRACT

An attempt was made to enhance the water-sorption capacity of polymers of 2-hydroxyethyl methacrylate (HEMA) by preparing its semi-interpenetrating polymer network (IPN) with a hydrophilic polymer such as poly(ethylene glycol) (PEG). The effects of various factors, such as history of the polymer sample, chemical architecture of the IPN, presence of salt ions in the swelling medium, and temperature of the swelling medium, were investigated on the water sorption kinetics of the IPNs. The IPN was characterized by IR spectral analysis and various structural parameters, such as molecular weight between crosslinks (M_c), crosslink density (q) and number of elastically effective chains (V_e), were evaluated. The IPNs were also assessed for their antithrombogenic potential.