Gel formation in ionomers

A theoretical study of the phase diagram of ionomer solutions in water is presented. These systems show two phase transitions: a demixing transition and a gelation. The demixing transition is studied using Flory's theory of polymer solutions. The gelation concentration always scales as the overlap concentration $\text{c1}$; the dependence of the phase boundaries on temperature and on the fraction f of metallic groups along the chain is studied. At high temperatures, in a good solvent regime, c_gel is proportional to $\text{f}{}^{\mathrm{<mtext>-8</mtext><mtext>5</mtext>}}$; at lower temperatures c_gel is proportional to f^?1.     

Effects of functionality and temperature on gel points in random polymerisation

First, the relationship between gel point and average functionality for an RA₂+R′B_f type polymerisation has been investigated by measuring the product of extents of reaction at gelation (α_c) for sebacoyl chloride (SC)/polyoxyproplyene (POP)diol/POP triol mixtures reacting at various initial dilutions in diglyme as solvent at 60°C. Intramolecular reaction always delays gelation and a generalisation of the Ahmad-Stepto gel point expression has been used to interpret the gelation data in terms of the ring-forming parameter λ′_ab. From the variation of λ′_ab with initial dilution, values of b, the effective bond length of the chain forming the smallest ring structure, have been derived. It is found that b decreases with average polyol functionality (f_w). This decrease apparently compensates for the increase in λ′_ab with f_w, so that ring formation is less sensitive to functionality than may have been expected. It is found that the Ahmad-Stepto expression does not predict a consistent relationship between λ′_ab, f_w and the gel dilution of reactive groups. Second, the effect of temperature on the gel point has been studied by measuring α_c for SC/POP triol mixtures reacting at various initial dilutions in diglyme as solvent at 27° C, 40° C and 60° C. At a given temperature, b decreases as triol molar mass increases, indicating that the POP residue of the chain forming the smallest ring structure is more flexible than the SC residue. This result is in keeping with those from previous investigations,^1,2 For a given triol, α_c decreases as temperature increases, indicating an increase in chain stiffness with temperature. Values of d In <r²>/dT are derived and found to be larger than those for linear chains.     

On the polycondensation reaction of Aa-BbCc type

Summary The curing theory for polycondensation reaction of A_a-B_bC_c type is investigated in detail to give gelation condition explicitly. Furthermore, a recursion formula for evaluating the polymer moments is obtained. This formula is suitable for both pre-gel and post-gel.     

Dynamic viscoelastic behavior of triple helical Lentinan in water: Effects of concentration and molecular weight

The dynamic viscoelasitc behavior of Lentinan, one triple helical β-(1 → 3)-d-glucan from the fruiting body of Lentinus edodes, in water was investigated as a function of concentration and molecular weight at 25 °C by using dynamic rheology. It was revealed that the shear storage moduli (G′), viscous loss moduli (G″), and the dynamic complex viscosity (η^∗) exhibited strong dependence on concentration and molecular weight. At low concentrations, the Lentinan/water systems displayed liquid-like behavior with G′ lower than G″ at low frequencies and crossing-over at high frequencies. With increasing concentration, the elastic response of the Lentinan/water system was stronger than the viscous response, leading to the conclusion that the Lentinan/water systems displayed a predominantly solid-like behavior. The gel point (c_gel) was determined from Winter-Chambon method (frequency-independence of tan δ). The most important point is that the c_gel was much lower than some synthesized polymers and other flexible polysaccharides, which may be attributable to the high stiffness of triple helical Lentinan and strong intra- and intermolecular interactions among polysaccharide chains. Furthermore, a decrease in molecular weight leads to a sharp increase of c_gel. The dynamic strain sweep measurements proved that the gelation of Lentinan in water is induced by the extremely entangled and stiff triple helices forming continuous network, and the Lentinan gel is structurally more like a solution that is unable to flow within a timescale of usual observation.     

Dynamic mechanical properties of some polyurethane-acrylic copolymer interpenetrating polymer networks

Dynamic mechanical properties have been investigated for interpenetrating-network systems based on polyol-cured polyurethanes (PU) and 2 to 1 n-butyl acrylate-n-butyl methacrylate (Ac) networks. The systems were formed simultaneously (SIN) from all of the precursors and reactants for both networks in the same vessel, and sequentially (SIPN) by swelling a precured PU with the reactants that will form the Ac network. If the Ac network is formed after gelation of the PU, the IPNs are transparent and appear to have single T (tan δ_max) between those of the homonetworks; visible-phase separation occurs if the Ac is intentionally polymerized prior to PU gelation. Damping curves were lower and broader and the T (tan δ_max) and rubber moduli were higher for the SIN than for the SIPN systems. Up to 65 percent Ac, the T (tan δ_max) data for both SIN and SIPN fit the Gordon-Taylor equation if a T (tan δ_max) for the Ac homonetwork 7°C higher than observed is used, suggesting a higher crosslink density for the Ac network under these conditions. The differences in properties of the SIN and SIPN are assumed to be dependent on sample homogeneity and upon the presence of a tin catalyst in the SIN preparation. This can result in limited Ac-network formation and consequent phase separation before PU gelation has occurred, and the catalyst may also increase the extent of interaction, such as grafting or hydrogen-bond formation between the networks.     

Effects of temperature on elastic behavior of short compact polymers

In this paper, we study further to explore the effects of temperature on the elastic behavior of short compact polymers. Average conformations and thermodynamics statistical properties at various temperatures T are calculated here. Different chain lengths N and elongation ratio λ are also considered simultaneously. From the plots of f and f_U vs. elongation ratio at low temperature, we can know that compact polymers are more close to the native states. With temperature decreasing deeply, polymer chains have the tendency to form globular structures. The results are concluded from: the ratio of 〈L₁²〉/〈L₂²〉 increase abruptly with temperature decreasing at low temperature, and both characteristic ratio 〈R²〉/Nb² and average energy per bond 〈U〉 decreases abruptly with temperature decreasing at low temperature, here L₁², and L₂² are the eigenvalues of the radius of gyration tensor S (L₁²≤L₂²). We also analyze the relationship between the heat capacity C_V and temperature T for different chain lengths in the process of tensile elongation. The coil-to-globule transition temperature T_c can be estimated from the location of the peak on the heat capacity plot as a function of temperature. The plots of 〈R²〉 as a function of chain length N at different temperatures are also shown, and the correlation 〈R²〉∼N^α is obtained at T>T_c or T<T_c, while at T=T_c, the plots are irregular, here α depends on temperature and elongation ratio simultaneously. Elastic force (f), energy contribution to elastic force (f_U), and the ratio f_U/f are also discussed at various temperatures. These investigations may provide some insights into elastic behaviors of compact polymers at different temperatures, especially at low temperature.     

Shear-induced gelation of associative polyelectrolytes

Copolymer of N,N-dimethylacrylamide (DMA) and acrylic acid (AA) was functionalized with pendant alkyl groups. Their dynamic mechanical properties in aqueous solution were investigated using continuous shear and oscillatory shear. Shear flow showed an abrupt divergence of the viscosity at a critical shear stress (σ_c). Oscillatory shear showed, with increasing applied stress, slight shear thinning followed by strong shear thickening above σ_c. The effect of the polymer concentration and the oscillation frequency (ω) was investigated. The behaviour at all concentrations and frequencies was fully determined by the product of the oscillation frequency and the terminal relaxation time (τ) of the systems at rest. Master curves of the data determined at different concentrations and frequencies were obtained if the reduced shear modulus was plotted versus the reduced applied stress at constant ω.τ. The effect of shear increased with decreasing value of ω.τ. At low frequencies the storage shear modulus crossed the loss modulus with increasing shear. A model is proposed for this phenomenon of shear-induced gelation.     

Application of the percolation model to gelation of an epoxy resin

The percolation model has been applied to the study of gelation of the TGDDM-DDS system (tetraglycidyldiaminodiphenylmethane–diaminodiphenylsulfone) at a mass concentration of 100–30. For each temperature the experimental viscosity curves are satisfactorily described by a percolation law. Using the degree of chemical reactions, X, as a variable, a very clear change in the reaction mechanism with temperature can be shown. Then a rate of advancement of effective reactions, Y, is defined. This value only takes intermolecular-type reactions into account, and is probably the only variable on which viscosity depends in a percolation law: η = B(1 ? Y/Y_c)^?p. We obtain Y_c= 0.45 and p= 2.0. Comparing X_c and Y_c at the gel point, we obtain information on the proportion of intramolecular reactions with temperature. It is also demonstrated that the critical percolation threshold agrees closely with the gel point determined experimentally on log G″= f(t) curves.     

Experimental evidence for trapped chain entanglements: their influence on macroscopic behaviour of networks

The swelling and elastic properties of poly(dimethyl siloxane) networks prepared by end-linking and subsequently swollen in heptane and toluene have been investigated as a function of the volume fraction, v_c, at which networks are generated. Increases in both swelling degree and shear modulus with v_c demonstrate the increase in number of trapped entanglements with v_c. The results may be described by a simple scaling law approach.     

Violation of the power-law dynamic mechanical behaviour at the gel point threshold in non-stoichiometric epoxide systems

Summary The dynamic mechanical behaviour of fully cured off-stoichiometric epoxy systems prepared from poly(oxypropylene)diamine (Jeff D-400) or -triamine (Jeff T-403) and diglycidyl ether of Bisphenol A (DGEBA) with initial ratios of reactive amine (NH₂) and epoxide (E) groups, r _H= (2[NH₂])/[E] ranging from 2.4 to 4.3 was investigated in the gelation threshold region. The evolution of the dynamic behaviour of two stoichiometric samples with r _H= 1 with reaction time, t _r , was also studied. The critical ratios for gelation, r ^c _H, of fully cured samples were determined from extraction experiments (r ^c _H= 2.54 for Jeff D-400/DGEBA and r ^c _H= 4.15 for Jeff T-403/DGEBA systems, respectively). For both stoichiometric critical gel (CG) structures obtained by changing the curing time t _r , a power-law rheological behaviour (G′∼ G″∼ωⁿ, G′ and G″ are the storage and loss moduli, respectively, ω is angular frequency and n is a critical exponent) with the loss tangent, tan δ= G″/G′ independent of frequency, was found. On the other hand, both CG off-stoichiometric systems with r ^c _H ratios show a small dependence of tan δ on ω, so that the critical power-law behaviour is not exactly obeyed. More complex CG structure in these samples, formed due to differences in the structure growth process, was suggested to account for violation of the power-law behaviour. Received: 4 December 1998/Accepted: 10 March 1999     

Dynamics and microstructure of charged soft nano-colloidal particles

The microstructure and rheological properties of swellable nano-particles consisting of cross-link methacrylic acid/ethyl acrylate were examined using dynamic light scattering (DLS) and rheological techniques. A unified semi-empirical approach for predicting the viscosity of dilute and concentrated systems was proposed, where a variable specific volume, k was introduced to convert the mass concentration to effective volume fraction. The viscosity data for four different microgel systems showed excellent agreement with the modified Krieger-Dougherty model. The parameters, c₀ and m for the expression, k−k_min/k₀−k_min=[1+(c/c₀)²]^−m as a function of degree of neutralization (α) were determined. We observed that c₀ decreases with α, while m increases with α. The validity of the new approach was compared against the theoretical model for determining the effective volume fraction, and excellent agreement was observed.     

Influence of cross-link density on the properties of ROMP thermosets

A norbornene-based cross-linker was synthesized and mixed at different loadings with two separate monomers for self-healing polymer applications: 5-ethylidene-2-norbornene (ENB) and endo-dicyclopentadiene (endo-DCPD). The monomer/cross-linker systems were polymerized by ring-opening metathesis polymerization (ROMP) with Grubbs' catalyst. The thermal-mechanical properties of the polymerized networks were evaluated by dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC) and the curing process was monitored by parallel plate oscillatory rheometry. The viscosities of the pre-polymer blends are shown to be adequately low for self-healing, and exhibit a high ROMP reactivity to form cross-linked networks with enhanced thermal-mechanical properties. The addition of cross-linker increases the glass transition temperature (T_g) and the storage modulus both above and below T_g. The storage modulus increase above T_g is used to estimate the molecular weight (M_c) between entanglements or cross-link sites for both ENB and endo-DCPD-based networks. The cross-linker also greatly accelerates network formation as defined by the gelation time.     

A study of intramolecular reaction and gelation during non-linear polyurethane formation

Intramolecular reaction and gelation in reactions of a poly (propylene oxide) triol and hexamethylene di-isocyanate in benzene at 70° have been investigated. The numbers of ring structures formed in the pre-gelation region have been evaluated from cryoscopic measurements of M_n and overall extents of reaction of isocyanate groups. It is found that intramolecular reaction increases with initial dilution, and at a given dilution is a maximum for equimolar concentrations of reactive groups. Again, at a given initial dilution, more intramolecular reaction occurs than for linear polymerisations. Various ways of presenting the results are discussed, and one of them in particular, the extent of intermolecular reaction, p_ch, as a function of overall extent of reaction of the minority group, p, gives useful linear relationships. Also, by combining gelation and intramolecular reaction in terms of plots of p_ch vs. p, a distinction can be drawn between what may be termed the chemical and physical gel points. Finally, values of the Flory-Huggins interaction parameter, X, have been determined from the cryoscopic data. These show fairly normal behaviour - they are generally less than 0.5 — with some dependence on the density of hydroxyl groups and the proportion of polyoxypropylene units present. Such behaviour is in sharp contrast with that found previously for poly (ethylene-oxide)/hexamethylene di-isocyanate systems.     

Structural evolution,sintering behavior and microwave dielectric properties of Al(1-x)(Si0.5Zn0.5)xPO4 ceramics

Al_(1-x)(Si_0.5Zn_0.5)_xPO₄ (0 ≤x≤0.6) ceramics were prepared via solid state reaction process. Their structural evolution, sintering behavior and microwave dielectric properties were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM) and with a network analyzer. Phase pure AlPO₄ could not be obtained for the undoped composition. However, microscopically homogeneous single phase solid solution formed within the compositional range of 0 < x ≤ 0.05. Immiscibility with two-phase structure within apparently single phase solid solution could be observed for other doped compositions (0.1 ≤ x ≤ 0.6). Small level of doping with (Si_0.5Zn_0.5)³⁺ (x≤0.4) stabilized the orthorhombic cristobalite-like AlPO₄ (C-AlPO₄) phase; while further doping led to the transformation from orthorhombic α-C-AlPO₄ into cubic β-C-AlPO₄ phase. The doping with (Si_0.5Zn_0.5)³⁺ considerably improved the sinterability and reduced the sintering temperature to ?900 °C when x = 0.6. The dielectric permittivity slightly increases and the Q × f value decreases with the increasing doping concentration. All composition demonstrate low permittivity (?_r ?4) and negative value of τ_f. Good combined microwave dielectric properties with ?_r ?3.9, Q × f?25,000 GHz and τ_f ? -25 ppm/^oC could be obtained for the x = 0.2 composition after sintering at 1200 °C/2h.     

Preparation of poly(N-isopropylacrylamide) hydrogel beads by circulation polymerization

Thermosensitive poly(N-isopropylacrylamide) hydrogel (NIPA hydrogel) beads have attracted much attention due to their applications in reaction and separation processes. This study focuses on the preparation of millimeter-sized, monodispersed NIPA hydrogel beads, for which a novel circulation polymerization technique is proposed. The method involves the drop-wise addition of a pre-gel aqueous solution into swirling silicone oil through a nozzle, and the subsequent conventional free-radical polymerization of the suspended pre-gel droplets, which drifts with the swirling oil. NIPA hydrogel beads that are 3.0 mm in diameter were successfully prepared with a very narrow distribution under fundamental conditions with no coalescence of the pre-gel droplets. The circulation polymerization technique improves the residence time and can be applied to a polymerization system that requires a long gelation time. The size of the resultant hydrogel beads corresponds to the size of the pre-gel droplets that are delivered from the tip of the nozzle, and can be controlled by adjusting the size of the nozzle.     

Effect of chain length distribution on thermal characteristics of model polytetrahydrofuran (PTHF) networks

A series of model polytetrahydrofuran (PTHF) networks were synthesized via end-linking reactions of α, ω-allyl PTHF oligomers with a stoichiometric tetrafunctional crosslinker. The telechelic PTHF oligomers were synthesized by living cationic ring-opening polymerization of tetrahydrofuran followed by a termination reaction with allyl alcohol. Networks thus prepared have well-controlled architecture in terms of the inter-crosslink chain length (M_c) and chain length distribution: resulting in unimodal, bimodal and clustered structures. Unimodal network was prepared by using polymer chains of same molecular weight, bimodal networks were synthesized by using two groups of polymer chains with different average molecular weights, and the clusters are prepared by incorporating clusters of networks with small molecular weight chains in a network matrix made of longer chains. Thermal characteristics of these model networks were investigated as a function of crosslink density, as well as inhomogeneities of crosslink distribution using DSC. We demonstrate that glass transition temperature (T_g) and crystallization behavior (melting temperature and crystallinity) of the networks are both strongly influenced by crosslink density (M_c). By comparing the unimodal, bimodal and clustered networks with similar average M_c, the effects of inhomogeneities in the crosslink distribution on the thermal properties were also investigated. Results show that inhomogeneities have trivial influence on T_g, but strongly affects the crystallization behavior. Moreover, the effects of the content ratio and length ratio between long and short chains, and the effects of cluster size and size distribution on the thermal characteristics were also studied.     

Particulate processes in freshly prepared silver iodide hydrosols part II. Sedimentation analysis of the sols

Negative stable silver iodide hydrosols prepared in statu nascendi were investigated by the method of sedimentation analysis. This investigation has been carried out in order to evaluate the assumption that the primary formed particles of stable, negative silver iodide hydrosols prepared in statu nascendi are monodispersed, and that the primary particles aggregate into secondary monodispersed particles by a second-order kinetic process. On the basis of experimental results, by measuring unsettled fractions, f^M_Σ, of AgI after centrifugation as a function of ω²t_c and ageing time t_A, it is proved that the primary formed particles of sols are really monodispersed and that their aggregation into monodispersed secondary particles is a second-order kinetic process. A radiotracer technique for the determination of fractions f^M_Σ was used.     

Crosslinked epoxies: Network structure characterization and physical–mechanical properties

A homologous series of epoxy resins, based on the digylcidyl ether of bisphenol-A, were reacted with stoichiometric quantities of m-phenylenediamine (mPDA) to form networks with varying crosslink densities. Infrared spectroscopic analyses revealed that the networks were formed predominantly by the epoxy—amine addition reactions with little or no OH-etherification. The ultimate glass transition temperatures were inversely proportional to the epoxy chain mol wt, as predicted by a model based on the assumptions of additivity and redistributivity of free volume. The average mol wt between crosslinks, M?_c, determined from the dynamic mechanical shear moduli, agreed to within 15 to 18% with the values predicted by the reaction stoichiometry. The glassy-state modulus did not exhibit any M?_c dependence above room temperature, however, the modulus—temperature plot for all the networks exhibited a discontinuity near ?50°C with a steeper slope below ?50°C than above it. The change in slope occurred over the same temperature interval as the β-transition temperature of the networks. The discontinuity in the modulus—temperature plot can be attributed to the freezing of the localized motions of the molecular groups responsible for the β-transition. © 1992 John Wiley & Sons, Inc.     

The correlation between N deficiency and the mechanical properties of the Ti2AlNy MAX phase

The role of X deficiency on the mechanical properties of MAX phases was studied by synthesizing Ti₂AlN through powder metallurgy in stoichiometric and sub/extra-stoichiometric nitrogen compositions. XRD analyses and ab initio calculations indicate that nitrogen vacancies result in a lattice contraction predominantly along the c-axis. The elastic moduli and intrinsic hardness of substoichiometric Ti₂AlN_0.9 measured from nanoindentation tests are shown to be slightly smaller than that of Ti₂AlN. The key mechanical indexes, bulk (B), shear (G) and Young’s (E) moduli as well as the hardness variation are calculated in density functional theory, and show different responses depending on the concentration of N vacancies. This joint experimental and theoretical study provides a full understanding of the energetics, chemical bonding, electronic structure, and mechanics of the N deficient MAX phases which would increase the application of nitride ceramics.