The glassy state,ideal glass transition,and second‐order phase transition

According to Ehrenfest classification, the glass transition is a second‐order phase transition. Controversy, however, remains due to the discrepancy between experiment and the Ehrenfest relations and thereby their prediction of unity of the Prigogine‐Defay ratio in particular. In this article, we consider the case of ideal (equilibrium) glass and show that the glass transition may be described thermodynamically. At the transition, we obtain the following relations: and with Λ = (α_gβ_l − α_lβ_g)²/β_lβ_gΔα²; and The Prigogine‐Defay ratio is with Γ = TV(α_lβ_g − α_gβ_l)²/β_lβ_gΔβ, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of ΔC_V and Γ, the ratio may take a number equal to, larger or smaller than unity. The incorrect assumption of perfect differentiability of entropy at the transition, leading to the second Ehrenfest relation, is rectified to resolve the long‐standing dilemma perplexing the nature of the glass transition. The relationships obtained in this work are in agreement with experimental findings. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 143–150, 1999     

New catalysts for urea formation reactions. II. Catalytic activity of carboxylic acids

Carboxylic acids with weak acidities showed large catalytic activity. For instance, for chlorine-substituted acetic acid the activity increased with decreasing chlorine content. For benzoic acid derivatives, electron acceptor substituents, such as NO₂, CI, and OH, lowered the catalytic activity, while electron donor substituents such as alkyl and alkoxy groups increased it. Detailed study on the cure rate of polyureaurethane, with 2-methyl benzoic acid as a catalyst, showed that pot life (PL) and the minimum demolding time (DT) had a correlation with the catalyst amount [X] represented by the following equation: where A and B are constants. Further, use of appropriate amounts of the catalyst enhanced tensile strength at break for polyureaurethane.     

A kinetic model of persulfate–bisulfite-initiated acrylonitrile polymerization

The molecular weight distribution has been derived for a homopolymer polymerized in a continuous-feed reactor under homogeneous conditions. The derived equations are then compared with data obtained on polymers of acrylonitrile–co(vinyl acetate) prepared under heterogeneous conditions with the potassium peroxydisulfate–sodium bisulfite–iron redox system. The termination reaction is assumed to be effected completely by recombination of active radicals with no disproportionation. The only transfer reaction considered is the transfer-to-activator reaction The transfer and termination reactions produce polymers with different acid groups as endgroups. Each molecule, on the average, contains one sulfonate group, whereas the concentration of sulfate groups depends upon the extent of the transfer-to-activator reaction. The basic dye acceptance of the polymer depends on the number of acid groups in the polymer and hence on the activator and catalyst concentrations. Analysis of the basic dye acceptance and conversion data at a variety of catalyst and activator concentrations yields the following parameters at 50°C: k_p/k = 1.01 (1./mole sec)^1/2, k_tr/k_p = 0.2063, and k₁ [see eq. (1)] = 50.7 l./mole sec. Owing to the heterogeneous nature of the polymerization, the weight-average molecular weight of the polymer depends only on the activator concentration and the conversion and not directly on the catalyst concentration as predicted.     

Synthesis and characterization of polyacrylic acid/dexy 85 and polyacrylic acid/gum arabic adducts

Polyacrylic acid/gum arabic or polyacrylic acid/dextrin (PAA/GA or PAA/D) adducts were prepared by free radical polymerization of highly concentrated, partially neutralized AA using Na₂S₂O₈/Na₂S₂O₃ redox system in the presence of GA or D. Optimum reaction conditions, viz., AA, 6.76 mol/L; Na₂S₂O₃, 26.87 × 10^?3 mol/L; Na₂S₂O₈, 34.9 × 10^?3 mol/L; degree of neutralization, 20%; temperature, 90°C; and time 30 min, were utilized in preparing two adducts of each substrate (GA or D) at two liquor ratios (LRs; 1.25/1 and 6.3/1 L/K). The four adducts formed, viz., PAA/GA₁, PAA/GA_2, PAA/D₁, and PAA/D₂ (where 1 and 2 refer to the low and high LR, respectively) were found to be water soluble at all proportions. IR spectrum of these adducts confirmed the introduction of the COOH group onto their structures. Rheological properties of 7% aqueous solutions of these adducts, including Na‐alginate (Alg), showed that all are characterized by a non‐Newtonian, shear‐thinning, thixotropic behavior. Within the range of shear rate studied, the apparent viscosities of these solutions followed the descending order: PAA/D₂ > PAA/D₁ > Alg > GA₁ = PAA/GA₂. Completing neutralization (Na form) of adducts to 100% results in a remarkable enhancement of their apparent viscosities, so that they follow the descending order, depending on the shear rate: © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 4290–4300, 2006     

Thermal conductivity of simple gases at normal pressures

Thermal conductivity measurements available in the literature for simple gases at normal pressures (approximately 1 atmosphere) were used to obtain the product k^*λ, where the parameter, λ =M^1/2T_c^1/6/P_c^2/3. Separate relationships between k^*λ and T_R resulted for monatomic, diatomic and triatomic gases. The relationships for monatomic gases can be expressed as follows For the diatomic and triatomic gases, linear relationships resulted, when at the same reduced temperatures, their k^*λ values were plotted against (k^*λ)_m on log-log coordinates. These relationships can be expressed in equation form as follows and Thermal conductivities calculated with these relationships have been compared with experimental values and produce an average deviation of 2.8% for the monatomic gases (219 points), 4.3% for the diatomic gases (282 points) and 4.6% for the triatomic gases (242 points). In this treatment, helium and hydrogen do not follow the general pattern and consequently these substances have been treated separately.     

A one-point intrinsic viscosity method for polyethylene and polypropylene

A statistical analysis of dilute solution viscosity data for a wide range of polyethylene and polypropylene samples in Decalin at 135°C has shown that the Martin equation fits the experimental data better than the Huggins equation at higher values of [η]c. A grand average k of 0.139 is applicable to both polymers. Based upon this, tables have been calculated permitting the ready determination of [η] from a single relative viscosity measurement at a known concentration. The Martin equation has been put into a universal form, permitting [η] to be calculated from a measured η_sp if k and c are known. Graphs relating η_sp to [η] are included for use of the Martin equation over wide ranges of both k and c. It was found that the Solomon and Ciuta equation fits the experimental polyethylene and polypropylene data, and the reasons for this are discussed.     

Effect of Molecular Symmetry and Intermolecular Halogen-Halogen Interactions on the Crystal Structures of Halogen-Substituted Benzoic Acids. X-ray Crystal Structure of m-Iodobenzoic Acid

The crystal structure of m-iodobenzoic acid is reported. The crystals are monoclinic, P2₁/c, with a = 6.220(3) Å, b = 4.689(2) Å, c = 26.67(1) Å, β = 101.80(3)°, Z = 4, C₇H₅IO₂. The structure has been determined by direct methods and refined to R 0.026 for 1288 reflections recorded with an automatic single crystal diffractometer. The structure is composed of essentially planar hydrogen-bonded dimer units with significant intermolecular iodine-iodine contacts. The configuration of the dimer unit is transoid. Since this is the penultimate member of the family of mono-halogen-substituted benzoic acids its structure is compared with those previously reported. In particular, the effects of differences in molecular geometry of the o-, m-, and p-isomers and the strengths of the intermolecular halogen-halogen interactions are surveyed. The geometry of the carboxyl group of m-iodobenzoic acid in the solid state and the carbonyl absorption in the Ftir spectrum of the crystalline acid at room temperature suggest the presence of dynamic proton isomerism as has been recently found by other investigators in crystalline benzoic acid and some of its derivatives.     

Studies on melt spinning. III. Velocity field within the thread

The velocity field within a molten spinning thread was analyzed quantitatively by solving the equations of continuity and momentum for Newtonian liquids. In solving the equations, the viscosity was assumed known and was given by the expression where x and r are distances in cylindrical coordinates. A series solution in velocity v having the expression was obtained when several simplifying assumptions were made on the equations. The series solution was found to converge when cr² < 1 is satisfied. μ₀e^βx and ν₀e^αx above are tangents on semilog paper at x = x to the macroscopic viscosity and velocity profiles μ(x) and ν(x) which were computed separately by means of a technique developed previously by the author.^1,2 The value c was derived from the temperature profile across the thread at x = x computed separately using another technique developed by the author.³ The above series solution showed numerically that under most conceivable spinning conditions the velocity field within the thread is for practical purposes flat across the thread and, in addition, purely extensional.     

Modified van der waals equation for the dense gaseous and liquid regions from PVT data for methane

PVT measurements available in the literature for methane in the gaseous and liquid regions were used with the van der Waals equation of state, to obtain values of the internal pressure parameter, a, where the covolume parameter was taken as b = v_c/3. The conditions covered temperatures from 114.53°K (T_R = 0.599) to 611°K (T_R = 3.20) and pressures up to 3000 atm (P_R = 65.50). A dimensionless relationship was developed for the dependence of the parameter a on density and temperature for the gaseous and liquid regions. Density values for methane were calculated from the resulting equation and were compared with the corresponding experimental values to produce an average deviation of 0.26% (791 points). This relationship also enabled the accurate prediction of density values for substances having similar critical compressibility factors as methane (z_c = 0.289). For neon and ammonia, this relationship was found to have a limited applicability.     

Synthesis of Allylarenes via Catalytic Decarboxylation of Allyl Benzoates

A catalyst system consisting of the palladium(0) complex Pd₂(dba)₃ and tri(p‐tolyl)phosphine was found to efficiently promote the decarboxylation of allyl benzoates with formation of allylarenes. This catalytic C O activation followed by extrusion of carbon dioxide and C C bond formation represents a sustainable alternative to traditional waste‐intensive cross‐couplings. The scope of the transformation includes allyl and cinnamyl esters of various ortho‐substituted benzoic acids. For particularly activated substrates, the palladium catalyst can optionally be replaced by an inexpensive nickel complex.

     

Adaptation of van der waals equation of state to the gaseous and liquid behavior of argon: Its application to simple substances

Utilizing the fact that the co-volume parameter, b = v_c/3, van der Waals equation of state has been reduced to the form where β = a/P_cv²_c and z = P_cv_c/RT_c. PVT data for argon, extending into the liquid region, have been utilized to establish the cohesive pressure parameter a as a function of temperature and density. This dependence is expressed in equation form and has been used to predict the PVT behavior of argon in its gaseous and liquid states, with an average deviation of 1.35% (250 points). The deviations resulting from this relationship for substances having similar z_c-values (z_c ≈? 0.291) were found to be of this order of magnitude.     

The shape of a fluid drop approaching an interface

The shape of a fluid drop approaching an interface does not change appreciably with time and is very close to the equilibrium dimensions, in spite of the large pressure gradient which is present in the draining film. This is because the net vertical force due to the excess pressure in the draining film above that in the drop is identical with that for an equilibrium film being zero for a plane interface and —2Rσ sin² ? for a deformable interface. Employing this result in a force balance around the drop which is independent of the bulk interface shows that the area A of the draining film between a fluid drop of volume V and a deformable fluid-liquid interface is given by where σ is the interfacial tension and Δρ the density difference between the drop and surrounding fluid, 1/b is the curvature at the top of the drop and h is the distance between this point and the edge of the draining film which is inclined to the horizontal at an angle ?. When the interface is a rigid plane the overall curvature 1/R of the draining film and the volume v enclosed by it, together with the angle ? are all zero. The limiting cases of the expression for very small and very large drops agree with those previously established for both deformable and rigid interfaces. An approximate expression which applies when cV^2/3 (where c = Δρg/σ) is between 0.6 and 13.5 and which gives A to within ± e% is where for a rigid plane interface and for a deformable interface When the densities of the drop and bulk heavy fluids are equal, but their respective interfacial tensions σ₁₂ and σ₂₃ with the light fluids are different, the expression becomes which estimates A/V^2/3 to within about ± 25% for σ₁₂/σ₂₃ in the range 0.11 to 9.0 and cV^2/3 (where c = Δρg/σ₁₂) between 0.6 and 13.5.     

Synthesis,Thermal Decomposition,and Properties of [Mn(CHZ)3][C(NO2)3]2

A new coordination compound, [Mn(CHZ)₃][C(NO₂)₃]₂, was synthesized and characterized by elemental analysis, IR and UV spectra, and its crystal structure was determined by X‐ray single crystal diffraction. The crystal belongs to the triclinic system and space group with a=0.88737(18) nm, b=1.1804(2) nm, c=1.1936(2) nm, β=83.73(3)°, V=1.1121(4) nm³, Z=2, D_c=1.867 g cm⁻³. Every Mn(II) ion is six‐coordinated to three CHZ molecules through three carbonyl oxygen atoms and three terminal nitrogen atoms to form a distorted octahedral structure. Mn(II) ions, carbohydrazide ligand molecules, and trinitromethanide anions are jointed to a complicated three‐dimensional netted structure through coordination bonds, electrostatic forces, and extensive hydrogen bonds. The thermal decomposition character and mechanism was studied by DSC, TG‐DTG, and FTIR techniques. The non‐isothermal kinetics has also been studied on the exothermic decomposition by using Kissinger's method and Ozawa–Doyle's method. In addition, the impact, friction, and flame sensitivity data were determined. All properties data observed show that the title complex has high energy, good thermal stability, and moderately friction sensitivity.     

Differential scanning calorimetry analysis of thermoset cure kinetics: Phenolic resole resin

The Differential Scanning Calorimetry (DSC) trace for a commercial phenolic resole resin shows two distinct peaks. Assuming that these represent two independent cure reactions results in a kinetic model of the form: with κ_i = κ_io exp(-B_i/T). The Arrhenius parameters were estimated from a plot of ln(β/T) versus 1/T_p. The parameters, p, n₁, and n₂ were obtained by writing the DSC response predicted by the equation above in terms of a function which contains temperature as the only variable. with $ \theta _i = \left({1/\beta} \right)\int_{T_0}^T {\kappa _i dT \le r_i} $ dT ? r_i and r_i = 1/(1-n_i). Fitting this equation to the DSC response measured at a scan rate of 4°C/min obtains p ≈ 0.66; n₁ ≈ 0.55; n₂ ≈ 2.2; B₁ ≈ 8285; B₂ ≈ 7480; κ₁ ≈ 1. 12 × 10⁸ s^?1; κ₂ ≈ 0.99 × 10⁶ S^?1.     

Densities of hydrocarbons in their saturated vapor and liquid states

The Sum and differences of the saturated vapor and liquid densities of 23 hydrocarbons were used to develop the following reduced density relationships for these saturated states The hydrocarbons considered included n-parafins, olefins, diolefins, naphthenes, and aromatics. Constants β, γ, and δ, and exponent n were found to be dependent on,. Equation (a) can reproduce liquid densities with an overall average deviation of 1.1 % over the entire temperature range, while Equation (b) was found to apply only in the interval 0.900 ≤ T_R ≤ 1.00 with an average deviation of 2.2%. For temperatures of T_k < 0.90, the saturated vapor density was found to depend on temperature as follows where k and m were also found to be Z_c dependent. Values calculated using Equation (c), when compared with 81 available experimental densities for 12 hydrocarbons, produced an average deviation of 3.0%.     

Flammability and thermal properties of rigid polyurethane foams with additionally introduced cyclic structures

Flammability, smoke evolution, thermal, and thermomechanical properties of low-density rigid polyurethane foams obtained from different aromatic polyols were investigated. The foams were prepared according to a standard formulation ensuring the same foam phosphorus content. Cellular polyurethanes with the best fire resistance were obtained from polyols containing disubstituted naphthalene and biphenyl rings. A linear equation was proposed to describe the influence of various structural units of the polyurethane (the content of cyclic structures C_c, nitrogen content C_N, and crosslinking equivalent M_c) upon its flammability, expressed in terms of its oxygen index (OI) Thermal stability of crosslinked polyurethanes was not found to influence significantly their thermomechanical properties, while crosslink density and the type and quantity of cyclic structures additionally introduced did have a pronounced effect upon these properties.     

The influence of fluid elasticity on wall effects for creeping sphere motion in cylindrical tubes

Experimental results are presented of wall effect for the slow motion of spheres in elastic, constant-viscosity liquids. The results are correlated in terms of diameter ratio for d/D < 0.3, and Weissenberg number We < 5. Weissenberg number is defined as We = 2θV_m/d, with θ the Maxwellian relaxation time (θ = N₁/2τγ). The wall effect is found to be adequately described by Newtonian expressions for small Weissenberg number, We < 0.01. For larger values of the Weissenberg number, We > 0.2, virtually no wall effect is discernible; the small effect observed is correlated by the wall factor expression The wall effect observed is ascribed to the influence of fluid elasticity alone, since all the fluids used were elastic to a greater or lesser extent, but showed no shear thinning.      

Versatility of a succinimidyl‐ester functional alkoxyamine for controlling acrylonitrile copolymerizations

Styrene/acrylonitrile (S/AN) and tert‐butyl methacrylate/acrylonitrile (tBMA/AN) copolymers were synthesized in a controlled manner (low polydispersity $ {{\overline M _w } / {\overline M _n }} $ with linear growth of number average molecular weight $ \overline M _n $ vs. conversion X) by nitroxide mediated polymerization (NMP) with a succinimidyl ester (NHS) terminated form of BlocBuilder unimolecular initiator (NHS‐BlocBuilder) in dioxane solution. No additional free nitroxide (SG1) was required to control the tBMA‐rich copolymerizations with NHS‐BlocBuilder, a feature previously required for methacrylate polymerizations with BlocBuilder initiators. Copolymers from S/AN mixtures (AN molar initial fractions f_AN,0 = 0.13–0.86, T = 115°C) had $ {{\overline M _w } / {\overline M _n }} $ = 1.14–1.26 and linear $ \overline M _n $ versus conversion X up to X ≈ 0.6. tBMA/AN copolymers (f_AN,0 = 0.10–0.81, T = 90°C) possessed slightly broader molecular weight distributions ( $ {{\overline M _w } / {\overline M _n }} $ = 1.23–1.50), particularly as the initial composition became richer in tBMA, but still exhibited linear plots of $ \overline M _n $ versus conversion X up to X ≈ 0.6. A S/AN/tBMA terpolymerization (f_AN,0 = 0.50, f_S,0 = 0.40) was also conducted at 90°C and revealed excellent control with $ \overline M _n $ = 13.6 kg/mol, $ {{\overline M _w } / {\overline M _n }} $ = 1.19, and linear $ \overline M _n $ versus conversion X up to X = 0.54. Incorporation of AN and tBMA in the final copolymer (molar composition F_AN = 0.47, F_tBMA = 0.11) was similar to the initial composition and represents initial designs to make tailored, acid functional AN copolymers by NMP for barrier materials. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Effects of strain rate and comonomer on the brittle–ductile transition of polymers

The effect of rate on the brittle–ductile transition of polymers can be given by an Arrhenius-type equation with activation energy between those of α and β transitions and given by where E_b is the activation energy for brittle-ductile transition, E_α is that for α transition, E_β is that for β transition, T_g is the glass transition temperature, T_b is the brittle–ductile transition temperature at 0.1 min.^?1, T_α is the α transition temperature at 1 cps, and T_β is the β transition temperature at 1 cps. The plots of T_b versus the weight fraction (w) of comonomer are sigmoidal, with an inflection point at w = 0.5.