Analysis of the melt viscosity and glass transition of polystyrene

The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T₀). Evidence that the glass transition is an isoviscosity state (log η_g ? 13) for lower molecular weight fractions (M < M_c) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; t_g = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT₀/dP = dT_g/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔV_g* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?_g/b = 0.03, but ?_g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dT_g/dP, one an exact derivation and the other an empirical correlation, are presented.     

Kinetics of high-intensity electron-beam polymerization of a divinyl urethane

The kinetics of high-intensity electron beam-induced polymerization of di(2′-methacryloxyethyl)-4-m-phenylenediurethane during the network formation has been studied up to complete gelation and up to 56% conversion of unsaturation. From experimentally determined gel fractions, rate of disappearance of unsaturation, kinetic chain length, and intensity dependence, it is proposed that the polymerization takes place in a swollen network where the growing chains undergo unimolecular termination, and where gel-gel reaction is prohibited. The rate expression derived is: In [α(1 ? g)^0.545] = In α0 ? 2.51 k_ik_pt/k_t where α is the total unsaturation and g is the gel fraction. The value of k_p/k_t is found to be 2.1 and that of G_R, the free radical yield per 100 eV absorbed, to be 16; these high values are ascribed to the high viscosity of the polymerizing system.     

A statistical measure of association and a series expansion of chain conformations

A simple, easily calculated, nonparametric statistic is described that can detect the presence of a functional relationship in bivariate data. Given a sample of data points (x,y), the statistic's value is nearly 1 if y is a linear function of x with little noise; it is greater than 1 if y is a nonlinear function of x; and it is close to 2 if x and y are uniformly and independently distributed. The statistic can be used to rapidly screen through large data sets to identify the most functionally related variable pairs. As an illustration, the statistic is used to detect relations between polypeptide conformational energy and functions of a series expansion for chain conformations.     

Estimation of molecular weight distribution based on chain length dependence of termination rate

When a chain length dependence of polymer-polymer termination is given by k_t,ns = const. (n^?2a + s^?2a) where n and s are the chain lengths for the polymer radicals and a is parameter, an instantaneous weight fraction of the non-reacting polymers is derived as: where h and k? are the kinetic parameters, p is a parameter depending on a, and p_n is instantaneous number-average chain length. Such a weight fraction corresponds to the experimental one over a wide range of conversion in the polymerization of styrene. On the scope of this correspondence, the polymer-polymer termination rate is estimated as: k?_t = 8πR₀D₁/100 ( = 4πR_sD_s) where R₀ is reaction radius between monomer radicals and D₁ is the diffusion coefficient of the monomer; R_s is reaction radius between segment radicals with n ? 100 and D_s is the diffusion coefficient of the segment. The Fujita-Doolittle theory applies to such a rate. Further, the rate also yields 1.5 × 10⁷1./mole-sec, which is the observable extent at conversions less than 0.2.     

Ferroelectric switching characteristics of 73/27 copolymer of vinylidene fluoride and trifluoroethylene

Ferroelectric polarization-reversal switching of vinylidene fluoride—trifluoroethylene copolymer with 73 mol % of vinylidene fluoride is investigated under a variety of conditions in an attempt to derive detailed information on the polarization reversal of the polymer. The electric-field dependence of switching time t_s obeys an exponential law. The temporal change of switching current density J is presented in the form J/(P_s ? P) versus time (P is the polarization, and P_s is its saturation value), which is free of the depolarization-field effect and discriminates in a straightforward manner between acceleration and deceleration of switching. Effects of the annealing of samples upon t_s are observed together with changes in the degree of crystallinity. Effects of space charge distribution upon t_s are investigated by applying two successive pulses, positive and negative, with varied intervals t_w between the two. The dynamics of space charge redistribution is elucidated from the t_w dependence of the t_s of the second pulse. The temperature dependence of t_s indicates that the switching becomes critically fast as the phase-transition temperature is approached.     

Numerical calculations of the viscoelastic properties of solutions of branched polymers based on the Zimm-Kilb theory

Numerical calculations were performed for the viscoelastic properties of dilute solutions of branched star polymers with equal branch lengths as formulated in terms of a bead-spring model by Zimm and Kilb without using the integrodifferential equation approximation method to calculate the eigenvalues. The complex modulus and complex viscosity were calculated as functions of frequency for various combinations of the number of branches f (4, 8, and 13), the number of beads in one branch N_b (= N/f; 20 to 100, where N + 1 is the total number of beads, N the number of springs in the molecule) and the reduced hydrodynamic interaction parameter h^* (= h/N^1/2 0.05 to 0.3, where h is the hydrodynamic interaction parameter of Zimm and Kilb). The frequency dependence of the complex modulus in the low-frequency range depends mainly on h^* and not on N_b if N_b is large enough, and it is very close to that calculated from the eigenvalues for h→∞ obtained by Zimm and Kilb, if h^* is about 0.25. As h^* decreases from 0.25, the frequency dependence gradually approaches that of the free-draining cash (h→0). Calculations may be carried out for h^* values somewhat larger than 0.25 and result in a frequency dependence that is not intermediate to the h → 0 and h → ∞ cases as evaluated by Zimm and Kilb. The physical meaning of such “super-non-free-draining” values of h^* is uncertain, however. The intrinsic viscosity ratio g′ = [η]_f/[η]_lin is an increasing function of h^* and changes very slowly with N. For h^* = 0.25, g′ is close to the non-free-draining limit for any value of N.     

Behavior of the electron density near an impurity

The behavior of the electron density n(r) and potential energy V(r) near the origin, where an impurity of charge Z is located, is studied using the Lindhard dielectric theory of the free-electron gas. The leading odd terms in the power-series expansion of n(r) and V(r) are obtained. It is shown that the derivative n′(0) = ?2Zn₀/a₀, where n₀ is the free-electron gas density and a₀ is the Bohr radius.     

The kinetics of the decarboxylation of n-butylmalonic acid in alkanols and amines

Rate constants and activation parameters are reported for the decarboxylation of n-butylmalonic acid in four normal alkanols (hexanol? 1, octanol? 1, decanol? 1, and dodecanol? 1) and in five amines (aniline, N-methylaniline, N-ethylaniline, N-n-propylaniline, and N-n-butylaniline). Both ΔH? and ΔS? of the reaction in both homologous series decrease regularly with increasing length of the hydrocarbon chain of solvent. If we compare data for the reaction in alkanol–amine pairs containing the same total number of carbon atoms in the molecule, we find that the ΔH? values are identical, but that the value of ΔS? is 0.8 eu/mole higher for the reaction in the amines as compared with the alcohol. The rate constant, at all temperatures, is 1.5 times as large in the amine as it is in the corresponding alcohol. Empirical equations are deduced relating the parameters ΔH? ΔS? ΔG? and k of the reaction to the parameters n and T, where n is the total number of carbon atoms in the solvent molecule and T is the absolute temperature. The results reported herein are compared with previously reported data for malonic acid.     

Role of diffusion in gel permeation chromatography

A theory is developed that describes the diffusion of solute into the gel particles during a gel permeation chromatographic experiment. The particles are treated as homogeneous spheres of radius a, into which diffusion takes place with diffusion coefficient D_s. The concentration in the mobile phase at any level at any time is supposed to be uniform throughout the cross-section of the column. It is shown that in the usual columns the effect of diffusion in the mobile phase is unimportant. A determinative quantity in the process is the parameter a²/D_st, where t is the time. For large values of a²/D_st an explicit expression for concentration versus time in the mobile phase at the end of the column is derived [eq. (26) and Fig. 1]. It shows a relatively long tail at large efflux volumes V, where the concentration varies at V^?3/2. For arbitrary values of a²/D_st the first three moments of the concentration versus time curve are calculated [eqs. (33)–(37)]. Pronounced skewness of the curve is found unless a²/D_st is small.     

On the use of multipole expansion of the Coulomb potential in quantum chemistry

Some features of the multipole expansion of the Coulomb potential V for a system of point charges are studied. It is shown that multipole expansion is convergent both locally in L₂(R³) and weakly on some classes of functions. One-particle Hamiltonians H_n = H₀ + V_n, where H₀ is the kinetic energy operator and V_n is the n-th partial sum of the multipole expansion of V, are discussed, and the convergence of their eigenvalues to those of H = H₀ + V with increasing n is proved. It is also shown that the discrete spectrum eigenfunctions of H_n converge to those of H both in L₂(R³) (together with their first and second derivatives) and uniformly on R³. © 1996 John Wiley & Sons, Inc.     

Investigation of the Chemo- and Stereoselectivity of the Ketene-Claisen Rearrangement

A novel type of ketene-Claisen rearrangement in which the precursor of the rearrangement is generated in situ by reaction of optically active allyl thioethers with dichloroketene is described. A characteristic feature of this rearrangement is the excellent chemoselectivity in favor of allyl thioethers vs. allyl ethers, i.e., exclusive chirality transfer of the allylic sulfur moiety is observed with 12, 13 , and 25--27 . The cyclic, optically active allyl thioethers (+)-(R)- 4 and (?)-(S)- 4 and the open-chain allyl thioethers 11--13 rearrange with in situ generated dichloroketene to the optically active thioesters (?)-(S)- 28 , (+)-(R)- 28 , and 31-33 , respectively. A chirality-transfer of > 99% in the cyclic cases (+)-(R)- 4 and (?)-(S)- 4 , and 96--98 % in the open-chain cases 11--13 is observed. Furthermore, the dichloroketene-Claisen rearrangement is characterized by a high asymmetric 1,2-induction. The chiral allylic sulfides 25--27 give the optically active thioesters 36--38 with a 1,2-induction > 99% as determined by NMR-shift experiments.     

Theoretical calculation of vertical ionization potentials of B2H6 by means of ΔESCF procedures

The vertical ionization potentials (IPS ) of B₂H₆ are calculated by means of the ΔE_SCF procedure, within the scheme of ab initio LCAO-MO-HF-SCF . The basis set used is LEMAO -3G. The scaling factors of the various atomic orbitals for the ground state and for the various hole states are optimized independently. The iteration procedure is specially designed to avoid the changes of the symmetry of the remaining occupied orbitals. The 1 ag (B1s) hole is found to be localized. The vertical IP of the 1 ag electron is calculated to be 196.5 eV, in fair agreement with experimental value. The D_2h symmetry is thereby broken and reduced to C_2V symmetry. The valence holes are found to be delocalized. The calculated vertical IPS are: 21.781, 16.974, 14.842, 14.389, 13.599, and 12.380 eV for the 2ag, 2b1u, 1b3u, 1b2u, 3ag, and 1b3g electrons, respectively. The agreement with experimental values is much better than the Koopmans' values. All these results are in favor of the concept that the nature of the convelent bond should be considered as a result of the mutual interactions and mutual conditioning between the wave nature of the electronic motion on the one side and the various attractive and repulsive factors on the other side.     

Mechanics of peeling of rubbery materials. II. Initiation and propagation of peeling

The peel strength of a joint with flexible materials bonded by an elastic adhesive was evaluated in relation to the fracture mechanism. It was found that initiation and propagation of peeling are governed by different mechanisms. Initiation (the formation of an initial crack) occurs when the maximum stress in the adhesive layer reaches a definite value. In this case, the strength f_i in a trousers-type peeling is given by 2f_i = y₀σ_b?_b, where y₀ is the half-thickness of the adhesive layer, σ_b is the tensile strength, and ?_b is the tensile elongation of the adhesive. On the other hand, propagation is governed by the surface energy of the adhesive. In this case, the peeling strength f_s is determined by a balance of energies. For trousers-type peeling it is given by 2f_s = Γ, where Γ is twice the surface energy. These results were verified experimentally.     

On p -nilpotency and minimal subgroups of finite groups

We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S ₄-free and every minimal subgroup of P ∩ G ^N is c-supplemented in N _G(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

Second virial coefficients of homopolymers and copolymers of butadiene and styrene in tetrahydrofuran

Second virial coefficients have been measured in tetrahydrofuran for a series of anionically polymerized narrow distribution homopolymers and copolymers of butadiene and styrene. The results fit the general empirical equation A₂ = M^?1/4(0.0216w_B + 0.00995w_S + Cw_Bw_S), where M is the polymer molecular weight, w_B and w_s are the weight fractions of butadiene and styrene, and C is a constant which is zero for block polymers and equal to 7.9 × 10^—3 for random copolymers. The equation is independent of the degree of 1,2 addition of butadiene and fits data on both linear and tetrachain star-branched polymers within experimental error.     

Scaling of some chemical properties of tetrahedral and octahedral molecules plus almost spherical C and B cages

It is shown that for tetrahedral and octahedral molecules the quantity a R _e /N ^1/3 is quadratic in the ratio z/N, where R _e is the equilibrium bond length, ze is the central charge and N is the total number of electrons. Some scaling properties for the ‘breathing’ force constant k are proposed for a series of 5 tetrachlorides.     

Effect of Cluster Deformations in the DLCA Modeling of the Sol-Gel Process

The diffusion limited cluster-cluster aggregation (DLCA) model is modified by including cluster deformations during aggregation, with a tuning flexibility parameter F. A three-dimensional computer simulation is presented, which starts from a collection of f-functional monomers randomly distributed in a cubic box with a volumic fraction c (concentration) and which uses the highly efficient bond fluctuation algorithm to describe the cluster deformations. It is shown that, for F 0, there exists a well defined threshold value of the volumic fraction below which the realization of all intra-aggregate bonding possibilities prevents the formation of a gelling network. For c > c _g , a true sol-gel transition occurs at a characteristic time t _g , after which an infinite cluster (which is self connected via the boundary conditions) appears. In contrast to DLCA, t _g does not increase as the box size increases. The transition at c _g is characterized by a divergence of the final clusters size for c<c _g and a divergence of the gel time for c>c _g . Several other numerical results are reported.     

Dipole moments of some substituted benzaldehydes. Conformational preference of substituents ortho to the aldehyde group

The dipole moments of a number of substituted benzaldehydes are measured in benzene solution. The angle which the dipole axis of the CHO group makes with the axis of rotation of the group is determined. The observed moments of the ortho-substituted benzaldehydes are compared with the moments calculated for free rotation as well as fors-trans ands-cis orientations of the -CHO group.o-Fluorobenzaldehyde exists mostly in thes-trans conformation.o-Chloro-,o-bromo-ando-nitro-benzaldehydcs also exist in thes-trans conformation; their observed dipole moments are even lower than the values calculated fors-trans forms, indicating mutual induction of the ortho substituents. Though 2,5-dichlorobenzaldehyde is expected to have the same dipole moment as benzaldehyde, the observed moment is significantly lower due to mutual induction of the ortho substituents. 2,5-Dimethylbcnzaldehyde has, however, almost the same moment as benzaldehyde. The dipole moment ofo-methoxybcnzaldchyde is considerably higher than the values calculated for boths-cis ands-trans conformations. An explanation is given for this.o-Hydroxybenzaldehyde exists exclusively in thes-cis form due to internal H-bonding.     

Radiation chemical studies of protein reactions: Effect of radiation on the breaking of secondary bonding in protein

The effect of radiation on the breaking of secondary bonding in protein was studied by measuring the viscosity change at different radiation doses and urea concentrations. An experimental equation for the viscosity change was obtained, and the observed behavior was explained on the basis of the molecular mechanism. The general equation for the viscosity change is given by η_red = A(X ? Be^?kx) + C log R, where η_red is the reduced viscosity of the solution, R is the dose of γ-radiation, X is the concentration of urea, and A, B, C, and k are adjustable constants.