General Method for Evaluation of Alternating Tendency in Copolymerization

A new method for deriving expressions for the mole fractions of alternating n-ads and the average lengths of the alternating sequences of n-component copolymers (n > 2) was developed based on the apparatus of finite Markov chains. These characteristics are considered as indexes of alternating tendency forn-component copolymerization. A specific property of n-component copolymerization (n > 3) compared with binary copolymerization is the fact that alternating n-ads might be constructed by two, three, or more types of monomeric units. In order to express this specific property of three and multi-component copolymers the term, alternating order, is introduced. The method developed in the paper permits the alternating indexes to be determined differentially in dependence of alternating order. Expressions for the average lengths and the compositions of all possible alternating sequences starting with a given monomer unit and ending with unit found only at that position, are derived as well. The alternating indexes for binary radical copolymerization of styrene and methyl methacrylate and for ternary radical copolymerization of styrene, methyl methacrylate, and acrylonitrile were determined.     

Azeotropy in Terpolymerization

This work deals with the determination of the various azeotropies in radical terpolymerization: unitary azeotropy (m_i = M_i); binary azeotropy (m_i/m_j. = M_i/M_j), and ternary or true azeotropy (M_j = m_j for j = 1, 2, 3). General analytical solutions are given which are easily handled by a computer. In addition, these calculations show the existence of pseudo-azeotropy where the deviation between polymer and monomer feed compositions is very small, not only at the beginning of the reaction, but also with increasing conversion.     

Deformation directions obtained from atom-atom potentials: molecular deformations in crystals

Forces of interatomic interactions F_ij calculated from atom-atom potentials as -dV_ij/dr_ij allow us to interpret angular deformations in the ring of sodium p-nitrobenzoate trihydrate. Calculations were made for distances r_ij between the ith and jth atoms belonging to different species less than the sum of the van der Waals radii of i and j. Calculations are based on very precise X-ray measurement of the cyrstal structure.     

Statistical branching of heterochains

A general theory for the statistical branching of heterochains is proposed on the basis of the random sampling technique. Consider a polymer mixture that consists of N types of chains whose weight fractions are w_i (i = 1, 2, …, N), and number- and weight-average chain lengths are P̄_np,i and P̄_wp,i, respectively. Suppose the transition probability that a branch point on a chain of type i is connected to a chain end of a type j chain is given by p_ij. When the branching density of chains of type i is ρ_i, the weight-average chain length is given by $\bar P_w = W\sum\nolimits_{m = 0}^\infty T ^m \sum\nolimits_{n = 0}^\infty {SU} ^n 1$, where S is the diagonal matrix whose elements are $S_{ii} = \bar P_{wp,i}$, 1 is the column vector whose elements are all unity, U is the transition matrix whose elements are given by $u_{ij} = \rho _i p_{ij} P_{np,j} ,T$ is another transition matrix whose elements are given by t_ij = (w_j/w_i)U_ji, and W is the row vector whose elements are w_i. Simpler expressions of P̄_w are presented for binary systems. In addition to the multicomponent systems, the present equation could also be used such as for free-radical polymerization with long-chain branching, by considering primary chains formed at different times as different types of polymer chains. For the prediction of the full molecular weight distribution, a Monte Carlo simulation method is used to illustrate the resulting distribution profiles.     

Atomic distributions in liquid copper-tin alloys

Abstract

Molten copper-tin alloys have been studied by X-ray diffraction, using a focusing theta-theta diffraetometer and Mo-Kα radiation (monochromator in the diffracted beam). Five alloys with 20, 35, 45, 55 and 78 atomic percent Sn, and pure Cu and Sn were measured at temperatures about 20 °C above the liquidus, and at 1100 °C. The total interference functions I(K), where K = 4π sin θ/δ, were obtained from the observed scattered intensities I_a(K) per atom and the theoretical atomic scattering factors. Splitting of the first peak in I(K) has been observed in the Cu-55 at% Sn alloy at the liquidus temperature.

The partial interference functions I_tj(K) at the liquidus temperature and at 1100°C were evaluated (assuming that they are independent of atomic concentration) using the five total I(K) of the alloys. The functions I_ij(K) are in reasonable agreement with those obtained by Enderby, North and Egelstaff from neutron diffraction data of a Cu-45 at % Sn alloy.

The reduced partial distribution functions G_ij(r) = 4πρ₀ r{g_ij(r) ? 1} and the probability functions g_ij(r) = ρ _ij(r)/c_j ρ₀, where ρ _ij(r) is the number of j-type atoms per unit volume at the distance r from an i-type atom, c_j is the atomic fraction of j-type atoms and ρ₀ is the average atomic density, have been evaluated by Fourier transformation of {I_ij(K) ? 1} K.

The electrical resistivities ρ _R of the alloys, calculated with the Faber-Ziman equation using the measured I_ij(K) and Animalu-Heine pseudo-potential elements U_i(K), are in good agreement with the experimental values of Roll and Motz. Assuming that U_i (2k _F) is independent of the values of the Fermi diameter 2k _F of the alloys, the concentration dependence of (3 - X)ρR, where X is the thermoelectric parameter measured by Enderby and Howe, is well reproduced when using the X-ray values of I_ij (2k _F).     

Residence times in kink sites and Markov chain model of alloy and intermetallic compound deposition

The concept of the residence time τ_ksp of an atom in a kink site has recently been suggested to understand the processes in electrochemical deposition of alloys and intermetallic compounds. Different kink sites with different residence times must be defined for alloys and intermetallic compounds. Based on this model, the finite Markov chain theory is applied to describe the selectivity of the growth process. An analytical relationship between the alloy composition and the metal ion concentrations in the electrolyte is derived. General model parameters are ratios g _i = K _ii/K _ij of equilibrium constants of the reaction of electrolyte ions with different kink sites on the surface (i, j representing different alloy components). These ratios are called selectivity constants. For simple conditions, the equation g _i ≈ τ_ii/τ_ij connects the g _i values with the residence times. The theory is tested in the deposition of alloys Co-Ni (anomalous co-deposition) and Ni-Mo (induced co-deposition). Additionally, Bi₂Te₃, an example of stoichiometric semiconductor deposition, is treated. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1216–1223. The text was submitted by the authors in English.     

Investigation of local density of monomer units and molecular dynamics in solutions of poly-4-vinyl-pyridine by the spin label technique

The local density of monomer units of the macromolecule (local density of the host molecule, ?_host) in poly-4-vinyl-pyridine solutions in ethanol was determined by the spin label technique. In dilute solutions, ?_host is considerably greater than the mean density of monomer units in the volume of the polymer coil; when the polymer concentration rises from 0.5 to 65 wt%, its increase does not exceed 30%. This indicates that the differences between polymer coil microstructure (mutual positions of monomer units close to a chosen unit) in dilute and concentrated solutions is small. The local density of monomer units of neighbouring macromolecules (guest macromolecules, ?_guest) is strongly dependent on the polymer concentration in solution. In dilute solutions, ?_host ? ?_guest; for polymer concentrations above 2–3 wt%, overlapping and interpenetration of macromolecular coils take place, local density of monomer units of neighbouring macromolecules rises and monotonously increases as polymer concentration grows. The concentration dependence of the local rotational and translational mobility of monomer units is determined by the local density of monomer units of the neighbouring macromolecules.     

Another look at the degree‐Kirchhoff index

Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees d_i ≤ D, for fixed D and all i, then for the index R′(G) = ∑_{i < j}d_id_jR_ij we show that We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N² ? 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Infrared band intensities: a comparative study of the transition moment matrix elements for the fundamental and overtones: Part II. Application to CO,HCl and OH

The various expressions considered in Part I for the transition moment matrix elements of fundamental and first two overtones are applied to carbon monoxide. The coefficients a_ij in the expressions R^io = Σa_ijp_j (where R^io is the transition moment integral for the O → i vibrational transition and p_j is the dipole moment derivative ?^jP/?XXX^j, XXX = (r — r_e)/r_e, r_e is equilibrium bond distance) are reported for i,j = 1, 2, 3. It is found that these coefficients do not vary by more than 5% when compared for the same i,j values in various expressions irrespective of the most exhaustive treatments used in deriving the original expressions. On the basis of the values of the coefficients obtained for CO, generalisations have been suggested on the effects of inclusion of mechanical and electrical anharmonicity to the intensities of fundamental and first two overtones. It is generally observed that the contribution of p'₁, is about 100 fold more than the contribution of p'₂, for R¹⁰. On the other hand the contributions of p'₁, and p, for R²⁰ and R³⁰ are of nearly equal magnitude but opposite in sign. The contribution of p'₁ to R¹⁰ is much higher than its contribution to R²⁰ and R²⁰. The various observations lead us to conclude that, whereas the effect of inclusion of mechanical anharmonicity on the intensity of the fundamental band is negligible, this effect is almost comparable to the effect of inclusion of electrical anharmonicity for the first two overtones. Simple forms of the a_ij expressions are applied to HC1 and OH to demonstrate the effect of variation of molecular constants on the a_ij values. On the basis of the observed trend in the values of these coefficients for CO, HCl and OH general remarks on the effects of hydrogen bonding on IR band intensities are given.     

Auswahl von Phasensystemen in der Lösungs-, Adsorptions- und Ionenaustausch-Chromatographie

In contrast to GC selectivity in LC is determined by the composition of both the stationary as well as the mobile phase. Therefore the main problem in LC results in selecting an appropriate phase system for the given separation problem. The selectivity factorα _ijis defined as the ratio of the capacity factors k′ _i k′_jof two solutes, which corresponds to the ratio of their distribution coefficients ^c K _i, ^cK_j. In LLC α _ijis determined by the relative solubility of the solutes in the two immiscible phases, which were prepared from binary or ternary liquid-liquid-systems. Secondary effects on retention are caused by the support. Two variations exist (LLC, Reverse-Phase-LLC) which differ in whether the polar phase is used as stationary or mobile phase, resp. In LSC the same phase variation is possible. Using a polar support and an unpolar solvent α _ijis governed by the relative strength of interactions between the solute molecules and the surface of the support. In Reverse-Phase-LSC, however, using an unpolar support and a polar solvent, these interactions are very weak and α _ijis mainly determined by the solubility of the solutes in the mobile phase. In IEC α _ijdepends on a set of parameters such as the type of ion-exchange matrix, its pore structure and its degree of crosslinking, resp., the type, surface concentration and distribution of functional groups, the type of the eluent ion, its concentration, the ionic strength and pH-value of the eluent, the temperature. Different methods have been developed in order to calculate the distribution coefficients of solutes for a given phase system.     

Product Relation of Copolymerization Reactivity Ratios

The copolymerization reactivity ratios designated as r_i = k_ii/k_ij are characteristic of thermodynamic conditions, such as temperature, pressure, and concentration, in which the temperature dependence has been demonstrated by kinetic procedures [14]. It is noted that in radical copolymerization the simple product of the reactivity ratios, e.g., r₁, r₂ generally tends to move toward unity with increasing temperature [2] and that for ionic copolymerization it is usually close to unity [5]. Such an inclination, however, involves some ambiguity in evaluating all the reported data [6] concerning the polymerization conditions.     

Copolymerizations of tetraethyl vinylidene phosphonate. Bisphosphonate units in the main polymer chain. II

This is the second part of the article with a subtitle “… The First Synthesis” published by us previously. For this, second part, we have chosen copolymers with low proportion of (‐b‐) units, as well as random copolymers with substantial proportions of (‐b‐) units. This is in contrast to the part I, in which we mostly described alternating copolymerization. In this article, radical copolymerization of tetraethyl vinylidene phosphonate (B) with several vinyl/ethylenic monomers (M₂), namely acrylamide, methacrylamide, methyl methacrylate, n‐butyl acrylate, n‐butyl methacrylate, and styrene has been described and reactivity ratios of monomers as well as the average length of the comonomer blocks (n) have been determined (r₁ = 0). It has been found, that (as it should be) there is a proportionality between r₂ (=k_m2M2/k_m2B) and n. Moreover, there is a proportionality between r₂ (or n) and the comonomer (M₂) “reactivity,” defined as the rate constant of M₂ addition to the styrene radical. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1614–1621     

Studies of Radical Alternating Copolymerization. I. Quantitative Determination of the Relative Reactivities between Free Comonomers and a Complex between Them; A Theoretical Treatment in Terms of Frontier Molecular Orbital Interactions. Application to Radical Maleic Anhydride-Vinyl Acetate Alternating Copolymerization

A simple quantitative determination of the ratio β₁ of rate constants k_ij corresponding to the addition of a complex or a free monomer on a same growing chain in alternating copolymerization was determined. The application of this method to the case of alternating maleic anhydride (A)-vinyl acetate (D) copolymerization give for β₁ = k_AC/k_AD and for β₂ = k_DC/k_DA (C refers to the complex) the respective values of 7 and 0. A complex was more reactive than A but less reactive than D toward a growing chain. In order to explain these reactivities, a frontier molecular orbital treatment was proposed. A good qualitative correlation with experimental results was obtained.     

Postgel properties in the statistical crosslinking of heterochains. I. Systems with N types of chains

The heterochain crosslinking model describes nonrandom crosslinking of polymer chains and is an extension of the classical Flory/Stockmayer gelation theory. We consider the postgelation relationship for the system consisting of N types of polymer chains, in which the probability that a crosslink point on an i‐type chain is connected to a j‐type chain is explicitly given by p_ij. The analytical solutions for the weight fraction of the sol, the number‐average and weight‐average molecular weights within the sol fraction, and the crosslinking density within the sol and gel fractions are derived for the systems, with each type of chain conforming to the Schulz–Zimm distribution. Illustrative calculations are shown for the systems consisting of two and three types of chains, and the obtained results agree with those from the Monte Carlo method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2333–2341, 2000     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

Bestimmung der Stabilit?tskonstanten von mehrkernigen Komplexen mit Hilfe einer spektrophotometrischen Methode

Zusammenfassung Es wurde eine allgemeine Gleichung für die Berechnung der Stabilitätskonstante von Komplexen L _mH_iM_nZ_j (Z=OH^–, usw.) abgeleitet und für Maximumbedingungen der Jobschen Kurve die Schwarzenbachsche graphische Methode so modifiziert, daß sie die allgemeine Bestimmung der Zusammensetzung und Stabilität von Komplexen L _mH_iM_nZ_j ermöglicht.

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Summary A general equation has been derived for the calculation of stability constants of complexes L _mH_iM_nZ_j (Z=OH^–, etc.). The graphic method of Schwarzenbach has been modified for maximum conditions of Job's curve in order to make possible the general determination of the composition and stability of complexes L _mH_iM_nZ_j.

     

Calculation of topological parameters of hyperbranched macromolecules synthesized via living radical polymerization

Numerical calculations of the kinetic model of synthesis of hyperbranched polymers in the living radical polymerization mode were performed. Analytical expressions were obtained that make it possible to predict the maximum yield of hyperbranched polymers and their topological parameters, such as the branching frequency; the numbers of living ends, monomer units and multiple bonds per macromolecule; and the degree of conversion at the gel point. The model is based on the use of a branching monomer M_m that contains m ≥ 2 polymerizable bonds in its molecule in combination with a monomer M₁ capable of forming linear chains only.     

Radical copolymerization of acrylic monomers. IV. Effect of substituents on the radical polymerization and copolymerization of phenyl acrylates

The kinetics of radical polymerization of phenyl, ortho-chlorophenyl, and para-chlorophenyl acrylates, as well as their copolymerization with methyl methacrylate, have been studied dilatometrically. The results obtained indicate that the overall rate of polymerization is affected by the flexibility of the growing radicals. However, the copolymerization of these monomers with methyl methacrylate gives overall rates rather similar for all three systems, being fundamentally regulated by the formation of reversible π complexes between the donor aromatic rings and the acceptor methacrylic double bonds. Dilatometric methods for the study of the copolymerization reactions have been tested and the corresponding binary bonding frequencies B_ij and conversion factors K_ij have been calculated for the copolymerization of ortho- and para-chlorophenyl acrylates with methyl methacrylate.