Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor(X) was introduced, the theoretical model could fit the tensile stress-strain data of mono-and bi-modal foam matrix well(Adj. R-Square = 0.9989, 0.9983). Parameters related to the polymer network, namely, average molecular weight(Mc) and volume fraction(ф) of chain segments between adjacent cross-linking points(network strands), were calculated by probabilistic method from the number-average molecular weight(Mn), vinyl content(w Vi) of the primary polysiloxanes and percent conversion(q) of vinyl groups. The primary and infinite strain amplification factors(X0, X∞) and decay exponent(z), introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams', we introduced another item, strain hysteresis item(H, related with the foam porosity and cell structure), into the statistical model as well. With the same above values of Mc,ф, X0 and X∞, the model could also fit the compressive stress-strain data of mono-and bi-modal foams well(Adj. R-Square = 0.9948,0.9985). Interestingly, the strain hysteresis items of the mono-and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.     

基于弹性统计理论的硅橡胶纳米复合材料本构关系的建立

基于考虑了悬垂链的橡胶弹性统计模型,通过引入应变放大因子,建立了硅橡胶纳米复合材料的基于微观机制的本构关系,其中利用硅橡胶分子信息(分子量M、乙烯基含量wt_(Vi)%)、乙烯基反应程度(q)估算获得本构方程中的交联点间链段分子量(Mc),网络链(network strands)体积分数(Φ)等参数,通过拟合确定了与纳米粒子相关的部分参数(初始应变放大因子X_0,极限应变放大因子X_∞,衰减因子z),对掺杂白炭黑的单组分及长短链配合硅橡胶拉伸应力-应变数据进行拟合,在采用相同X_∞,z值情形下,拟合曲线仍能与实测值符合较好(拟合的Adj.R-Square值分别为0.99576、0.99596)。基于微观物理机制的本构关系能够成为联系微观分子结构参数与宏观应力的桥梁,本文工作有望为更有针对性地改进和优化硅橡胶的性能提供依据。     

Nonsteady-State Model for Kinetics of Radical Chain Polymerization. 1. Direct Photoinitiation and Thermal Initiation with Constant Monomer Concentration

Chain radical polymerization with direct photoinitiatlon or thermal initiation and constant monomer concentration has been theoretically studied by dealing precisely with the kinetic differential equations. The expressions for molecular size distribution, number- and weight-average degrees of polymerization, and their dependence on the reaction conditions are derived in analytical form. A computation program allowed easy calculation of these parameters concerned with the resultant polymer.     

Reinforcement of Natural Rubber from Hydroxyl-Terminated Liquid Natural Rubber Grafted Carbon Black. I. Grafting of Acyl Chloride Capped Liquid Natural Rubber onto Carbon Black

Abstract

This paper deals with the grafting of acyl chloride capped liquid natural rubber (LNR–COCl) onto carbon black by the reaction of the acyl chloride group with the phenolic hydroxyl group on the surface. LNR–COCl was prepared by the reaction of hydroxyl-terminated liquid natural rubber (HTNR) with adipoyl dichloride. The percentage of grafting was estimated to be 18–21% depending on the grafting temperature and the molecular weight of HTNR used. It increased with an increase in the molecular weight of LNR–COCl. The LNR grafted onto carbon black was investigated by IR spectroscopy and by hydrolysis with a dilute THF solution of KOH. It was shown that LNR grafted onto the carbon black surface with ester bonds.     

Model for a three-center decomposition reaction. I. Perfluorodiazirine

A semiempirical approach has been used to evaluate rate parameters for a three-center decomposition reaction from the point of view of transition state theory, with perfluorodiazirine serving as the prototype molecule. Several activated complex models are considered in which the reaction coordinate is chosen as the ? NCN bending mode. The constraints imposed include the principle of concerted bond-order conservation in passing from the initial to the final state, and use is made of empirical bond order–bond length and bond order–force constant relationships. The geometric configuration of the transition state sought is one which conforms with the lowest energy path and is also consistent with the observed entropy of activation. The potential energy of activation is taken as the optimum difference in binding energies (based on the INDO method) between the transition and initial states, and the critical energy is obtained by applying a correction for the zero-point energy difference, derived from normal coordinate analysis. Satisfactory agreement is found in the case of the activated complex model for which the total bond order is conserved and bonds undergoing rupture are assigned a fractional bond order (FBO) of 2/3, derived from the postulate (FBO) = α/β whe re α(=2) is the number of bonds breaking, and β(=3) is the number of bonds undergoing change in the ring opening.     

Orientation of Polymer Chains in Dilute Solution under Shear: Effect of Chain Model and Excluded Volume

Summary: Polymer orientation in dilute solutions undergoing shear flow is investigated computationally by means of the Brownian dynamics simulation technique applied to the bead‐spring chain model. The dependence of the degree of orientation on the shear intensity is evaluated through a quantity called orientation resistance. All simulations were performed using non‐preaveraged hydrodynamic interaction (HI). The spring type (Gaussian or FENE) is shown to strongly determine the shear flow behavior of the chain orientation. Solvent quality (Θ, good or bad), represented by a suitable Lennard‐Jones intramolecular potential, does not affect the flow behavior but influences the values of the orientation resistance. Hence, the orientability of the polymer molecule is, in a way, related to the flow intensity.

Evolution of m_G (orientational resistance parameter, open circles are simulation, dashed line is Gaussian approximation) and m_τ (filled circles are simulation, dotted line is Gaussian approximation) with β for ideal Gaussian chains with N = 15.     

An Improved Approximation for the Primitive Model of the Electric Double Layer

Abstract

The primitive model for the one sided electrode interface consists of an electrode which is perfectly smooth and flat, and an electrolyte formed by charged hard spheres, all immersed in a dielectric continuum.

The early work of Gouy,¹ Chapman² and Stern³ is based on such a model, and in recent times it has received considerable attention by a number of researchers. Extensive computer simulations have been performed by Torrie, Valleau and coworkers.⁴ The approximate integral equations which have been used to compute the density and voltage profiles and differential capacitance can be divided into four groups. Mean Spherical Approximation (MSA) and its generalization (GMSA),^5,6 the Hypernetted Chain (HNC) and derived equations,^7,8 the Modified Poisson-Boltzmann's (MPB)⁹ and the Born-Green-Yvon (BGY)^10,11 type theories.     

Determination of Chain Transfer Constant for Solvent When the Viscosity of the Polymerizing System Is Considered Important

Abstract

The chain transfer constant of the polymethyl methacrylate radical for N,N-dimethylaniline was determined in two solvents, benzene and dimethyl phthalate. Plots were made using1/P_n=k_t°R_p/k_p ²[M]²η + C_S1 [S₁]/[M] + C_S2 [S₂]/[M] +C_M where η=viscosity of monomer-solvents mixture, k_t°=rate coefficient of termination when η=1 cP, S₁=benzene or dimethyl phthalate, S₂=N,N-dimethylaniline, and other symbols have their usual meanings. The plots agreed well for the two solvents. If the plots were made without considering the viscosity term, two separate lines resulted for the two solvents. Thus it is essential to consider the viscosity of the polymerizing system in the analysis of chain transfer reactions when the termination reaction is diffusion-controlled and the viscosities of the monomer and solvent differ markedly.     

Parameter Estimation for the Constant Capacitance Surface Complexation Model: Analysis of Parameter Interdependencies

Results of extensive application of the 2-pK constant capacitance surface complexation model (CCM) to surface charge data of a range of minerals in 0.1Melectrolytes are summarized where the program FITEQL has simultaneously been used to study the interdependence of the involved optimized parameters.To illustrate representative results, surface complexation and goodness of fit parameters are given as a function of the capacitance value (C). For all (ca. 150) tested data sets, one of three patterns is observed, two of which do not allow a unique parameter set to be obtained.The results indicate that the optimized site density parameter is relatively insensitive to a wide variation ofC; optimized site density is rather low in this range of (higher)Cand tends toward maximum proton uptake in the respective data set which in turn will be close to sometimes experimentally observed saturation levels. At low and with further decreasingCa steep increase of site density may occur; in this case, ΔpK_astrongly increases after a ΔpK_aminimum. Alternatively at lowC, ΔpK_amay continue to decrease and site density decreases simultaneously after a site density maximum. The observed patterns can be explained by the constraint ofCon the electrostatic correction factor.Linear correlation coefficients (which are very useful parameters but do not receive much attention) show that in the region of lowC, the optimized parameters become fully correlated, which finally causes nonconvergence in parameter optimization. In the region where the optimized site density is not significantly affected by a decrease inCthe optimized parameters are more weakly correlated. When site concentration is co-optimized high correlation between adjustable parameters suggests that it is preferable to have an estimate for this parameter.Overall, it can be stated that substantial difficulties were observed in the effort to obtain unique (and thus meaningful) parameters for the CCM in about 60% of the data sets treated.     

Energy-consuming micromechanisms in the fracture of glassy polymers. I. Chain scission in polystyrene

The number of chain scissions per unit area that occur during the fracture of partially annealed latex films from M_n ? 180,000 g/mol polystyrene particles of about 275 Å radius were measured and correlated to annealing times. A curve with four regimes was found. At short annealing times the curve is nearly flat, in what is called the chain pull-out regime. In the second regime, the number of chains broken per unit area increases with a 0.8 power of annealing time as entanglement of the diffusing polymer chains increases in neighboring host particles. This is in good agreement with Wool's theory which predicts a 0.75 power dependence. Then, after reaching a peak, the number of scissions decreases in the third regime, indicating a change in fracture mechanism. The number of chain scissions increases again in the fourth regime, as final healing of the film interface takes place. Fracture surface analysis reveals a rough surface for short annealing times and a smooth surface for longer annealing times. The number of polymer chain scissions per unit area of fracture surface showed no dependence on initial molecular weights for t ? τ_r where t and τ_r are annealing and relaxation times, respectively. The number of chain bridges crossing a unit area of interface was suggested as the basic molecular property. © 1992 John Wiley & Sons, Inc.     

Overall crystallization kinetics of thin polymer films. General theoretical approach. I. Volume nucleation

A general theoretical approach of the overall crystallization kinetics of thin polymer films is developed. This new model makes it possible to calculate the evolution of the transformed volume fraction anywhere in the film, whatever the cooling conditions are. In its isothermal limit this model is equivalent to previous approaches which have been well verified by a computer simulation. In conclusion, it is pointed out that both isothermal and anisothermal determinations of crystallization kinetic parameters are greatly dependent on the sample thickness.     

Kinetic Studies of Block Polycondensation. I. Aggregation of Various Carboxylic Acids in Solvents of Low Dielectric Constant

Self-association of benzoic, octanoic, and octadecanoic acids was studied in solvents with a range of dielectric constants between 2.3 and 10. The number-average molecular weights were determined by means of vapor pressure measurements and were carried out at temperatures ranging from 25 to 90° C. It appears that, in these solvents of low dielectric constant, carboxylic acids are present mainly as molecular or ionic aggregates.     

A Numerical Model for the Optimal Vulcanization of 2D Polar Rubber Compounds Using Microwaves

A numerical model is presented for the optimal vulcanization of 2D extruded polar rubber with microwaves and peroxides. Magnetron power and curing time are used as the input production parameters, and the output mechanical property selected for optimization is the average tensile strength of the item. A 2D thick weather strip is analyzed to validate the model. The electric field is evaluated by means of Yee cells (FDTD approach) and suitably inserted in Fourier's heat transmission law, thus allowing point‐by‐point temperature profiles to be determined. The temperature is then used to evaluate the degree of peroxidic reticulation, and thus the final tensile strength. A so‐called alternating tangent approach based on the bisection method is finally proposed to estimate the optimal magnetron power and curing time.

     

Rubber networks containing unattached macromolecules. I. Linear viscoelastic properties of the system butyl rubber–polyisobutylene

Mixtures of butyl rubber with polyisobutylene (molecular weights 0.055 and 2.3 × 10⁶) up to 50% by weight were crosslinked by sulfur, leaving the polyisobutylene molecules free to reptate in the butyl rubber network. Linear viscoelastic properties were measured in shear creep for periods up to 5 × 10⁵ sec at 25°C and oscillating shear deformations from 0.1 to 3 Hz, at temperatures from 2 to 63°C. Comparison with the properties of a butyl rubber crosslinked without polyisobutylene showed contributions to creep and mechanical loss attributable to the reptating species. Comparison with the properties of polyisobutylene (higher molecular weight) showed that the relaxation times associated with the reptating species in the upper part of the terminal zone are the same for different polyisobutylene contents (25% and 50%) and for 100% polyisobutylene in which no permanent network is present; their contributions to modulus appear to be proportional to the volume fraction of polyisobutylene to a power of about 2/3. The time required in stress relaxation for the portion of the modulus attributable to the reptating species to decay to half its plateau value is, based on the two molecular weights employed, proportional to the polyisobutylene molecular weight to the third power. The magnitude of the associated mechanical loss and its location on the frequency scale can thus be controlled independently.     

Population Balance Model for Batch Gravity Separation of Crude Oil and Water Emulsions. Part I: Model Formulation

A population balance model for the separation of emulsions in a batch gravity settler is presented. Within the context of the model development, possible methodologies were elucidated for incorporating a) the physical properties of the bulk liquids, b) the physical properties of the phase interface, and c) the presence and functioning of interfacially active compounds. The model presented explicitly accounts for interfacial coalescence and the deformation of the emulsion zone due to the dynamic growth of the resolved dispersed phase; interfacial coalescence is modeled in terms of physically meaningful film drainage models and an approach for incorporating the accumulated buoyancy force in the dense packed layer is also discussed. Hydrodynamically hindered sedimentation is also considered in the model. The model is well suited to predict experimental batch settling data, especially data obtained from low-frequency NMR measurements of emulsion destabilization. The model predicts the evolution of the volume fraction of the dispersed phase at any axial position and time in the separator. Furthermore, the model predicts the location of the resolved dispersed phase interface as a function of time. Additionally, for any axial position and time in the settler, the model predicts the evolution of the average number density of droplets, the average volume/radius of droplets, the standard deviation of the droplet volume/radius, and the rate of growth of the droplets. The model is compared directly with experimental data for crude oil separations in Part II of this article.     

Size Exclusion Chromatography of Associating Systems. I. The Theoretical Model

Abstract

Block copolymers in dilute solutions in selective solvents form micelles via closed association which is characterized by equilibrium between unimer and n-mer. A simple theoretical model has been proposed describing the behavior of such a system in the size exclusion chromatography (SEC). Chromatograms have been calculated varying association number and relative rates of association and dissociation. The results are compared with those of Coll's theory for SEC of surfactants and Gilbert's theory of associating systems.