Molecular models of polymer networks and constitutive equations of rubber elasticity

Equilibrium elastic behaviour of crosslinked polymers (networks) is analysed both from the macroscopic (phenomenological) and microscopic (molecular) points of view. Molecular mechanisms possibly responsible for non-linear rubber elasticity are discussed. They include: conformational entropy of network chains at small and large extensions, hindered rotation of such chains and intra-chain point interactions, dipole-dipole interactions between asymmetric chain segments, and topological constraints leading to chain entanglement.     

Experimental tests of entanglement models of rubber elasticity: 1. Uniaxial extension-compression

The predictions of several entanglement models of rubber elasticity for the uniaxial stress-strain response of crosslinked polymer networks are examined. It is found that the Gaylord tube model and the Flory constrained junction fluctuation model both agree well with the experimental data.     

Elasticity of real networks: Comparison of molecular theory with experiments

Predictions of the theory of elasticity of real networks are compared with results of experiments. The shape of the stress-strain curve for networks in the dry and swollen states and over wide ranges of strain, both in tension and compression, agrees with results of calculations based on the theory. The theory is also in close agreement with results of multiaxial stress-strain experiments and with the predictions of the degree of crosslinking obtained from measurements of the modulus. The theory may additionally be applied to the analysis of birefringence. The assumption of the linear additivity of the elastic and mixing free energies in a swollen network leads to results which are in agreement with experimental findings on different crosslinked systems.     

拓扑学原理在化学化工中的应用

从拓扑学原理出发,引入了拓扑指数的概念,并用拓扑方法研究分子结构-理化性质、结构-活性、结构-保留及阴离子表面活性剂结构-HLB值定量关系。同时探讨了拓扑化学反应控制原理及其在合成化学与工业生产中的应用。     

Effect of the processing conditions and the addition of trans-polyoctenylene rubber on the properties of natural rubber/styrene–butadiene rubber blends

In this study, the influence of the processing conditions and the addition of trans-polyoctenylene rubber (TOR) on Mooney viscosity, tensile properties, hardness, tearing resistance, and resilience of natural rubber/styrene–butadiene rubber blends was investigated. The results obtained are explained in light of dynamic mechanical and morphological analyses. Increasing processing time produced a finer blend morphology, which resulted in an improvement in the mechanical properties. The addition of TOR involved an increase in hardness, a decrease in tear resistance, and no effect on the resilience. It resulted in a large decrease in the Mooney viscosity and a slight decrease in the tensile properties if the components of the compounds were not properly mixed. The results indicate that TOR acted more as a plasticizer than a compatibilizer. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Predicting the solubility of 1,1-difluoroethane in polystyrene using the perturbed soft chain theory

In this study, the solubility of 1,1-difluoroethane in polystyrene is correlated and predicted using the perturbed soft chain theory (PSCT) and compared with the experimental data in the literature. For correlation, a binary interaction parameter is determined using the experimental solubility data. For prediction, however, the data at infinitely dilute solvent concentration region from inverse gas chromatography (IGC) are used only in determination of the binary interaction parameter. The results were comparable with the experimental data in both cases. © 1998 SCI.     

The structure and elasticity of polyurethane networks: 1. Model networks of poly(oxypropylene) triols and diisocyanate

The equilibrium mechanical and optical behaviour of networks prepared from poly(oxypropylene) triols (PPT) and 4,4′-diphenylmethane diisocyanate (MDI) at various initial molar ratios of reactive groups, $\text{r}{}_{\mathrm{<mtext>H</mtext>}}\text{=}\text{[}\text{OH}\text{]}\text{[}\text{NCO}\text{]}$, in the range 0.6 < r_H < 1.75 have been investigated. The reaction proceeded at 80°C and in the presence of an organotin catalyst to a high conversion of minotirty groups (0.96–1.0). A comparison between experimental and theoretical (based on the theory of branching processes) dependences of the equilibrium modulus, G_e, on r_H or on the sol content, w_s, led to the following conclusions: (1) In the range r_H ? 1 the theory adequately describes experimental dependences, while in the range r_H < 1 excess crosslinking takes place, obviously due to the formation of allophanate groups. (2) In PPT networks with a higher molecular weight (M_n = 2630), G_e is about twice the theoretical value for the front factor A = 1, which is interpreted as a contribution due to permanent interchain interactions. (3) In networks of lower PPT (M_n = 708), experimental G_e values lie between the theoretical ones calculated for A = 1 (affine deformation crosslinks) and $\text{A =}\text{1}\text{3}$ (phantom network). (4) The difference between the eperimental and theoretical moduli for $\text{A =}\text{1}\text{3}$ may be adequately described by using Langley's concept of trapped entanglement contribution (for networks of the longer triol quite satisfactorily, for those of shorter PPT with some systematic deviation) with the same proportionality constant. (5) For correlations between the experiment and theory a generalized plot of the reduced modulus of the weight fraction of the gel proved to be useful.     

Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis

The Edwards-Vilgis (EV) slip-link theory (1986) derives the elastic free energy of a rubber-like network model containing stable and sliding network junctions (crosslinks and slip-links) and predicts both low-strain softening and high-strain hardening. The four-parameter stress-strain relations calculated by the theory for geometrically different deformation modes up to high strains were tested experimentally using published biaxial stress-strain data on simple covalently crosslinked networks. For networks with low degrees of strain softening and low extensibilities, the experimental dependencies could be described rather well but, generally, a simultaneous satisfactory fit to uniaxial, pure shear and equibiaxial data was not obtained. Systematic experiment-theory deviations exceeding 10% were observed and some of the parameters had a tendency to assume values lying outside the reasonably expected range. The prediction of a pronounced maximum in the strain dependence of stress supported by slip-links seems to be a reason for the discrepancy. Also, modeling of the high-strain singularity in entropy is done in the EV theory using a rather simple approximation. As a result, the finite extensibility contribution to the stress of a slip-link-free network model becomes improbably high and significantly exceeds that following, at a given modulus and locking stretch, from the rigorously derived Langevin-statistics-based eight-chain-network elasticity theory of Arruda and Boyce.     

高分子橡胶材料老化的影响因素及应对措施分析

高分子材料是一种十分先进的材料,无论在国内还是在世界范围内都发挥着举足轻重的作用.虽然应用广泛的高分子材料在当今社会占有着十分重要的作用,但实际上,老化问题是高分子材料需要面临的问题.本文将详细分析与探讨高分子材料所面临的老化问题,对高分子材料老化的影响因素分析,并以一些实际情况为依据,对其提出一些相应的解决措施.     

Toward understanding the effect of substitutes and solvents on entropic and enthalpic elasticity of single dendronized copolymers

Using single molecule force spectroscopy (SMFS), we have investigated the single chain elasticity of a series of dendronized copolymers, whose original backbone is styryl dendron and maleic anhydride. The amilysis reaction of maleic anhydride introduces amide and carboxyl side groups. Hence, the copolymer bears three type side groups, Fréchet type dendrons, amides and carboxyls. The single chain elasticity of the polymers in tetrahydrofuran (THF) and chloroform (CHCl₃) has been obtained, respectively. There is no hysteresis between the stretching and relaxing force curves of individual polymer chain, indicating that the elongation is carried out at the equilibrium condition. The force curves can be fitted well by the modified freely jointed chain model, which suggests that the elongation of the polymer chain is controlled by the entropic elasticity in the low-force region but dominated by enthalpic elasticity in the high-force region. The polymer with first-generation dendrons shows different elasticities in the two solvents, which should result from the different hydrogen bonds of the dendronized copolymer in two solvents. When the dendron groups are changed to be second and third generations, the single chain elasticity of the polymers is the same in two solvents. Hence, the elasticity of the polymer chain can be different depending on the properties of side groups and solvents.     

黏土/天然橡胶纳米复合材料的制备及性能

利用乳液插层法制备了黏土／天然橡胶纳米复合材料,研究了该复合材料的力学性能、应力应变行为、耐磨性、气体阻隔性和耐老化性能。结果表明,黏土／天然橡胶纳米复合材料与高耐磨炭黑(N330)、白炭黑增强橡胶相比,邵尔A型硬度、定伸应力和撕裂强度较高,拉伸强度相当。黏土、N330以及白炭黑对天然橡胶的拉伸结晶有影响,填料用量对材料拉伸强度的影响存在最佳值。黏土／天然橡胶纳米复合材料具有良好的耐磨性、气体阻隔性和耐老化性能。     

Langevin-elasticity-theory-based description of the tensile properties of double network rubbers

A previously proposed and successfully tested constitutive equation denoted by the ABGIL code (a combination of the Arruda-Boyce equation based on the Langevin elasticity theory and a constraint term based on tube theories; strain-induced increase in the finite extensibility parameter is assumed) has been found to provide a good basis for quantitative interpretation of the stress-strain data recently obtained by Mott and Roland on double networks of natural rubber, prepared by introducing additional crosslinks (second network) into a first network stretched to various extents. Experimental information on properties of the first and second networks has been used to obtain their ABGIL parameters and to calculate, under the common assumption of additivity of contributions, the stress-strain properties and residual stretch of the resulting double networks. The predictive ability of the ABGIL equation has been found to be very good. Effects of the finite extensibility of network chains appear to be significant in double networks while the possible role of orientational crystallization cannot be excluded.     

Experiments on the small-strain behaviour of crosslinked natural rubber: 2. Extension and compression

Experiments were carried out to characterize the small-strain tension and compression behaviour of dicumyl peroxide crosslinked natural rubber. Strains that were smaller by an order of magnitude than any reported previously on natural rubber were achieved. Our results support the contention that the compression and extension moduli of natural rubber are different. A new finding is reported: that is, the moduli in tension and compression do not become constant but rather they increase significantly as zero deformation is approached.     

Heat capacity of polymer melts from the polymer chain-of-rotators equation of state

Recently, the chain-of-rotators equation of state derived from the rotational partition function was extended to polymers. Values of the three equation of state (EOS) parameters were obtained from fitting with experimental pressure–volume–temperature data and the parameters were correlated with the structure of the polymer repeat unit. In this article, the residual molar heat capacity derived from an EOS is added to the ideal gas heat capacity from Benson's group contribution method to obtain the polymer molar heat capacity at constant pressure, C_p. Predictions from the polymer chain-of-rotators (PCOR) using correlated parameters are compared with those obtained from PCOR, Sanchez–Lacombe, Flory–Orwoll–Vrij, and the perturbed-hard-sphere chain equations of state using parameters fitted from experimental data. Deviations of calculated C_p from the formula of van Krevelen for liquid polymers are likewise presented. With the correlations developed for its parameters, the PCOR offers the advantage of predicting the C_p for polymer melts from just the knowledge of the polymer's structure. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:841–848, 1998     

Comparative study of the elasticity and permeability of vulcanized films made with skim and cream natural rubber latex

The purpose of this study was to gain a clearer picture of the structure and properties of vulcanized films made with skim and cream latex from Hevea brasiliensis. The two properties targeted for this study were the elasticity of the films and their permeability to acetone. Surface characterization by atomic force microscopy revealed that vulcanization substantially modified the structure of the films compared to unvulcanized films. Unlike unvulcanized films, particle identity was retained in the vulcanized films made with cream latex, even after 4 weeks of aging. In addition, skim latex gave vulcanized films with greater elasticity than those obtained with cream latex. On the basis of the structural characterization carried out on the latex and films and information from the literature, the greater elasticity of the skim films arose from more entanglements between polyisoprene chains and associations between proteins. Despite differences in the structure, the acetone permeability was very similar for skim and cream vulcanized films. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Unlubricated rolling and sliding wear against steel of carbon‐black‐reinforced and in situ cured polyurethane containing ethylene/propylene/diene rubber compounds

The dry rolling and sliding friction and wear of ethylene/propylene/diene rubber containing carbon black and in situ cured polyurethane (EPDM+PUR_CB) were studied. For rolling and sliding tests against steel counterparts, different experimental conditions and tribotests were selected. The apparent network properties and phase structures of the rubbers were derived from dynamic mechanical thermal analysis and atomic force microscopy results. It was concluded that in EPDM+PUR_CB, both rubber phases, present in a 1 : 1 ratio, were continuous (interpenetrating network). The coefficient of friction (COF), specific wear rate (W_s), and heat development during the tribotests were determined. The carbon black and polyurethane contents did not much influence the COF in rolling wear tests. W_s of the ethylene/propylene/diene rubber containing carbon black went through a minimum as a function of the carbon black content. W_s of the EPDM+PUR_CB compounds decreased monotonously with an increasing amount of carbon black. The incorporation of polyurethane into the ethylene/propylene/diene rubber compounds decreased the resistance to rolling wear markedly. With carbon black filling of the ethylene/propylene/diene rubber–polyurethane compound, the COF and W_s increased and dramatically decreased, respectively, under sliding wear. The wear mechanisms were inspected with scanning electron microscopy and discussed as a function of recipe modifications and changes in the testing conditions. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Sulfuric acid treatment of ground tire rubber and its effect on the mechanical and thermal properties of polypropylene composites

Ground tire rubber (GTR) was modified by sulfuric acid in order to improve its compatibility with and reinforcement of a polypropylene (PP) matrix. Polymer composites PP/GTR were prepared by melt mixing at different concentrations, with a maximum of 50 wt % of GTR. Studies by Fourier transform infrared spectroscopy (FTIR), surface specific area by BET (Brunauer, Emmett, and Teller), and scanning electron microscopy were used to characterize the untreated GTR and treated GTR, while the mechanical and thermal properties of the PP/GTR composites were assessed to understand how the surface treatment of GTR affected the mechanical and thermal properties of the composite PP/GTR. FTIR revealed the presence of sulfonic groups on the surface of sulfuric acid–treated GTR, and BET analyses showed an increase of about 625% in the specific surface area as a result of the high porosity produced by the treatment. In all composites containing treated GTR, a higher Young's modulus was obtained than for composites containing untreated GTR. Particularly, an increase of about 275% in the Young's modulus was obtained in composites with treated GTR (40 wt %) against that containing untreated GTR. However, a more significant reduction of the elongation at break was observed in composites containing treated GTR than in those containing untreated GTR. Also, an increase of the crystallization temperature of PP as a function of GTR was observed by differential scanning calorimetry, but the crystallinity of the composites was reduced by the addition of both untreated and treated GTR. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44858.     

Blends of polypropylene with poly(cis‐butadiene) rubber. II. Small‐angle X‐ray scattering studies of the phase structure of immiscible blends of polypropylene with poly(cis‐butadiene) rubber

Pressed films of the blends of polypropylene (PP) with poly(cis‐butadiene) rubber (PcBR) were studied by IR spectra, small‐angle X‐ray scattering, and scanning electron microscopy. The problem of the interaction between different macromolecules in the blends of PP/PcBR is discussed by melt‐mixing at a temperature of 210°C using IR. X‐ray scattering from the relation of the phase was analyzed using Porod's law, and the interface layer thickness was calculated. The immiscibility of the blends of PP/PcBR was proved. The structure parameters, the correlation distance a_c, average chord lengths l?, and radius of gyration R?_g were obtained by the Debye–Buech statistical theory of scattering. Porod's index was calculated and the shape of the dispersed phase is discussed in relation to Porod's index in the blends. The morphology and structure of the blends were investigated by scanning electron microscopy. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2088–2094, 2002