Diffusion in polymers dependence on crosslink density

Kinetics of N-methyl pyrrolidone evaporation from swollen photo-crosslinked polyacrylate was monitored thermogravimetrically at temperatures ranging from 323 to 398 K. Crosslink density dependence of evaporation kinetics was investigated in photo-crosslinked polyacrylates with crosslinked density ranging from ≈1.2 × 10² to ≈1.7 × 10⁴ mol m⁻³ and number of main chain atoms between crosslinks ranging from ≈70 atoms to ≈6 atoms, respectively. As was shown, evaporation kinetics was controlled by the solvent diffusion in polymer. Activation energies of evaporation (diffusion) were deduced from the rate measurements at different temperatures. Apparent activation energy of evaporation decreased from 48.7 to 31.1 kJ mol⁻¹ with crosslink density increase. Activation energy of pure N-methyl pyrrolidone evaporation was 50.6 kJ mol⁻¹. Decrease of the rate of solvent diffusion and unexpected decrease of diffusion activation energy with increase of crosslink density of swollen polymer matrix was explained by decrease in polymer chain segments mobility, as indicated by Eyring’s approach to diffusion in polymers.     

Rheological properties of linear and crosslinked polymer blends: Relation between crosslink density and enhancement of elongational viscosity

Strain‐hardening behavior in the elongational viscosity of binary blends composed of a linear polymer and a crosslinked polymer, in which the molecular chains of the linear polymer were incorporated into the network chains of the crosslinked polymer, was studied. Blending the crosslinked polymer characterized as the gel just beyond the sol–gel transition point greatly enhanced the strain‐hardening behavior in the elongational viscosity, even though the amount of the crosslinked polymer was only 0.3 wt %. However, the crosslinked polymer, which was far beyond or below the sol–gel transition point, had little influence on the elongational viscosity as well as the shear viscosity. The stretching of the chain sections between the crosslink points was responsible for the strain‐hardening behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 228–235, 2001     

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.     

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.     

Energy transfer between samarium and europium in phosphate glasses

A study of energy transfer from samarium to europium in phosphate glasses was performed for a range of donor and acceptor concentrations corresponding to a donor-acceptor distance of 13–24 Å. The energy transfer probabilities were calculated. The mechanism of transfer was deduced by fitting the experimental decay curves to the theoretical curves obtained by Inokuti and Hiroyama. Theoretical transition probabilities based on Dexter's formula were calculated. It was inferred that the energy is transferred by a dipole-quadrupole mechanism which is assisted by phonons. It was possible to indicate the path by which the transfer takes place.     

Toughness of polymeric networks: The limited importance of crosslink density

Four series of polymeric model networks were prepared with bimodal chain length distribution between crosslink points and two types of dangling chains as network defects. In the last series the crosslink density was changed without a large change in the chemical composition. The fracture toughness of those networks were compared with that of the defect–free networks. The fracture toughness of the various networks is surprisingly little influenced by the introduction of defects. Neither bimodality, nor dangling chains, nor a high sol fraction alters the toughness of the network. A good correlation between K_Ic and the weight fraction of polyether is observed. A much smaller dependence of K_Ic on the strand density can be deduced. The yield stress is high and approximately invariant for all systems studied. It is concluded that the toughness of a polymeric network does not seem to be influenced by its perfection and only to a small extent by its degree of crosslinking.     

A generalized theory for the glass transition temperature of crosslinked and uncrosslinked polymers

A generalized theory for the glass transition temperature of crosslinked and uncrosslinked polymers has been developed, which takes into account the influences of end groups, branching, and crosslinking, and their functionality distribution. DiBenedetto's theory was found to correctly characterize the influence of crosslinks on the glass temperature. Normalized to constant crosslink functionality, the crosslink constant is a universal parameter suggesting that the entropic theory of glasses is applicable to crosslinked systems. Data on linear polymers and networks from the crosslinking of polymer chains, vinyl/divinyl-copolymers and step-growth polymers, such as polyurethanes, amine-cured epoxies, or inorganic glasses, are presented.     

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.     

Rheological analysis as a means for determining the silane crosslink network structure and content in crosslinked polymer composites

For evaluating the crosslink content of a polymer, gel content determination is a commonly used method. However, for crosslinked polymer composites containing particulate filler, the gel content may be overestimated due to partly trapping filler inside the gel portion. In this paper, parallel-plate rheology was used, together with the gel determination and FTIR measurement, for determining the silane crosslink network structure and content in crosslinked ethylene–octene copolymer composites. The effects of filler surface property on structure and content of silane crosslink are also discussed. The results show that a correlation plot between gel content, IR absorption index and crosslink density provides useful information on changes in silane network structure and properties of the crosslinked composites. The network structure formed (loose or tight network) shows a strong influence on the final tensile properties of the crosslinked products.     

The relationship between crosslink system, network structure and material properties of carbon black reinforced EPDM

The crosslink density and sulfur-ranks of crosslinks formed during vulcanization of a carbon black reinforced ENB–EPDM compound are analyzed as a function of the selected curing system: Conventional, Semi-Efficient, Efficient and Nitrosamine-safe. Each vulcanization system results in a specific crosslink concentration and sulfur-rank distribution: mono-, di- and polysulfidic of nature. Tensile properties, tear strength and compression set of the vulcanized materials turn out to practically only depend on overall crosslink density, as resulting from the particular curing systems and vulcanization times. All trends in properties coincide when plotted as a function of the overall crosslink density. Surprisingly, the crosslink distribution: the ratios of mono- to di- and polysulfidic crosslinks, has only a minor effect on these properties. The differences in sulfur-rank as a function of the chosen vulcanization system turn out to be too small for EPDM to have a significant effect.     

Mobility of the ring structure and the characteristics of crosslinked polymers: The structural effect of the eleven-membered ring and its homologs upon the dynamic mechanical properties and glass transition temperature of crosslinked diallyl succinate polymers

Dynamic mechanical properties and glass transition temperatures were measured for crosslinked polymers derived from diallyl succinate monomers. The mobility of the diester having an eleven-membered ring and of homologous structures which are introduced in the crosslinked polymer system, is discussed on the basis of the parameter for cyclization polymerization of a monomer, dynamic mechanical properties, and glass transition temperature. Control of the mobility of the ring structure and its homologous structures involved in the crosslinked polymers was attempted by modification of the substituent at the 1- or 1,2-position of diallyl succinate, and the diallyl succinate monomers were derived from the succinic acid and its derivatives: succinic acid, methyl succinic, ethyl succinic, and chlorosuccinic acids; cis-1,2-dicarboxylic acids of cyclopropane, cyclobutane, cyclopentane, and cyclohexane; cis-1,3- and 1,4-dicarboxylic acids of cyclohexane, and phthalic acid. The results obtained are explained well on the basis of the mobility of the ring and homologous structures.     

Reduced-variable mechanical characterization of styrene-butadiene rubber with varying crosslink density,temperature, and finite strain states

A single master logarithmic stress relaxation curve of reduced modulus as a function of reduced time is established for a styrene-butadiene rubber (SBR) system, accounting for the effects of crosslinking density, temperature, and time. The results from recent tests involving uniaxial and various biaxial strain states at finite strain levels may be represented by a unique strain-energy function W of the Valanis-Landel separable symmetric type, where the λ_i are principal extension ratios. These two representations demonstrate that the mechanical response of whole families of elastomeric materials may be predicted once a single member of the family is fully characterized.     

Structure-property relations in linear and crosslinked liquid crystalline polymers

This paper reviews structure-property relations in liquid crystalline side group polymers, as investigated by X-ray scattering of fibres, by small angle X-ray scattering in solution, by dielectric relaxation measurements and by melt rheology, as well as synthetic ways to “combined liquid crystalline polymers”. The synthesis of liquid crystalline elastomers from side group, main chain and combined liquid crystalline polymers is described. First structure-property relations are discussed.     

Investigating time–temperature superpositioning in crosslinked polymers using the tube‐junction model

This article examines the application of time–temperature superpositioning (TTS) in certain thermorheologically complex polymers using a recently developed phenomenological model that describes crosslinked polymer viscoelasticity based on fundamental physical considerations. The model's capability to calculate both isochronal temperature sweeps and isothermal frequency sweeps of storage and loss moduli allows us to simulate conditions typical of certain thermorheologically complex polymers. We use the model to generate modulus frequency sweeps over the limited range of frequencies that are typically accessible to experiments. We apply TTS to shift these sweeps along the frequency axis to construct master curves. The model master curves are then compared with the model's “true” moduli curves over the full frequency domain at the reference temperature. This comparison suggests that nonsuperposability may go unnoticed if we only rely on the smoothness of the storage modulus master curve. Superpositioning to achieve a smooth loss modulus master curve tends to be more reliable. This has serious implications for assessing the reliability of relaxation moduli and creep compliance master curves that have no associated loss component that can be used to assess the quality of superpositioning. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 127–142, 1999     

The two-electron integral transformation and two-body density matrix transformation

Ann ⁵ algorithm for the transformation of quantum-mechanical four centre functions is presented in a form best suited for computers having a virtual memory capability. Part of the work to be submitted for the degree of Ph. D. in the University of Newcastle-upon-Tyne.     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.