Description of oxygen permeability in various high polymers using a graph theoretical approach

Graph theory methods are shown to complement group additivity methods of predicting oxygen permeability in certain types of polymers. Graph theory is a topological approach that assigns a set of indices to a molecule to describe its structure. Since many physical properties of molecules depend upon their structure, graph theory indices can be used to describe important properties of molecules. In this work a set of graph theory indices are used to describe the property of a polymer based on a modified representation of the monomer unit. More specifically, Randic indices are used to describe the log of the oxygen permeability with 3.2% average relative error. Polymers comprising the basis set contain backbones of sp², sp³, or aromatic carbons, oxygen, or silicon and have substituents that contain chloride, fluoride, alkyl groups, hydrogen, oxygen, aromatic carbons, or chloro and/or fluoro substituted alkyl groups. The correlation coefficient (R²) (0 ≤ R² ≤ 1) of a nonlinear model is 0.91. The graph theory method for describing the oxygen permeability of these selected groups of polymers is in good agreement with that predicted by the permachor model. The permachor method makes oxygen permeability predictions based upon group additivity and distinguishes the degree of crystallinity of a polymer by empirically assigning different permachor (π) values to identical groups based upon the polymer crystallinity. The inability of graph theory to explain the remaining 9% of the scatter in the data is probably due to failure to incorporate into the graph theory model terms which quantify crystallinity.     

Rotational diffusivity of rodlike molecules in amorphous polymeric matrices

In this note, scaling laws for rotational diffusivity of dilute monodisperse rigid-rod molecules (guest rods) in semidilute amorphous polymer solutions (host molecules) are derived. The coillike matrix molecules are modeled as a collection of flexibly connected rigid subunits. This allows an analogy with the Doi-Edwards theory for monodisperse rigid rods in semidilute solutions to be used in the analysis. Very strong dependencies are predicted for the rotational diffusivity of the rods on host polymer volume fraction and rod length. In semidilute polymer solutions the coils dramatically hinder the rotational freedom of the rods for r² ? ψ_p^?1, r being the rod aspect ratio and ψ_p the polymer volume fraction.     

Light scattering and intrinsic viscosity investigation of polymethyl-3, 3, 3-trifluoropropylsiloxamer

Solution parameters for the polymer poly-γ-trifluoro-propylmethylsiloxamer has been determined in cyclohexyl acetate, methyl hexanoate, and ethyl acetate. Interpretation of data follows the theory of Fox and Flory. In contrast to poly-dimethylsiloxane, an increased steric hindrance to rotation about the siloxane bond occurs as evidenced by the characteristic ratio of root-mean-square end to end dimensions, (r₀² /r_0f² )^1/2, found to be 1.90 and 1.96 at 25.0 and 72.8°C, respectively. This increase is considered to be primarily due to nearest-neighbor interaction of the polar substituent on the silicon atom. The relation, [η]θ ∝ M^1/2, was observed to hold for this polymer system. The hydrodynamic model appropriate for the polymer is a random coil considerably more permeable to solvent flow than is generally reported for linear polymers. The universal parameter ? was determined to be 1.5 × 10²¹. The effect of temperature on polymer configuration is indicated to be negligible.     

Second virial coefficient of polymers in good solvents: The case of polyelectrolytes

A stepwise segment-by-segment cluster development of the interaction energy of two polymer coils at given distance leads to a closed expression, describing the second virial coefficient A₂ in terms of certain intersegmental contact probabilities. An approximate expression for A₂(α,z) in good solvents is then derived by using the uniform segment cloud model; the result being equivalent to that obtained by Flory. This expression is combined with the author's theory for α²(z) to give A₂(z), and then with a subsequent adaptation of that theory to polyelectrolytes, to derive the dependence of A₂ on ionic strength. The α²(z) and A₂(z) equations are both compared with recently reported experimental data for NaPSS.     

Equation for the interfacial tension between demixed polymer solutions

The theory of Cahn and Hilliard is used to derive an equation for the interfacial tension (free energy) between some demixed polymer solutions, applying a simple solution model treated by Debye in his theory of light scattering near the critical solution temperature. For a (symmetrical) system containing two polymers in a common solvent it is found that the interfacial tension is given by σ = (l/12^½)Ω_φp ²σ_r, where l is the Debye l parameter for the range of molecular interaction—here equal to (2S² )^½, where (S² )^½ is the radius of gyration of both polymers, Ω is a heat of mixing parameter for polymer-polymer interaction, φ_p is the total volume fraction of polymer and σ_r is a function of the ratio of temperature and critical solution temperature. The equation is in qualitative agreement with experiments of Langhammer and Nestler.     

Glass transitions in ionic polymers

The glass transitions of an ionic polymer in bulk have been studied as a function of the counterion for various homo- and copolymers. It is shown that the glass transition temperature can vary by as much as 530°C., from ?10°C. for the nonionic material to +520 for Ca²⁺ or Zn²⁺ substituted polymer. From simple electrostatic considerations, it is shown that a linear correlation should exist beween the glass transition and the ratio of the cation charge, q, to the internuclear distance, a, between cation and chain anion; for this particular material (the polyphosphate chain) the relation is T_g = 625(q/a) ?12 where q is in units of one electron and a is in A. If the data are interpreted in the light of the Gibbs-DiMarzio theory, it is seen that both the chain stiffness and the intermolecular energy increase in an approximately parallel manner as q/a increases.     

Molecular dynamics of a smectic liquid-crystalline side-chain polymer. The dielectric properties of aligned and nonaligned material studied over a wide range of frequency and temperature

The dielectric relaxation behavior of a nonaligned and an aligned liquid-crystalline (LC) polymer are reported for the ranges 10^?3.5 to 10⁵ Hz and 274–363 K. Multiple processes (δ and α) are observed that follow a Vogel equation for the temperature dependence related to the apparent glass transition temperature. The occurrence of these processes and the variation in their relaxation strengths as sample alignment is changed is interpreted in terms of a molecular theory for the dielectric behavior of a LC polymer that involves the director order parameter S_d, the mesophase order parameter S, the dipole moment components of the mesogenic head groups, and their associated relaxation functions.     

Morphology and interactions of polymer brush‐coated spheres in a polymer matrix

Using a real space implementation of the self‐consistent field theory, we calculated the morphology and interactions of spherical nanoparticles with radius R_p that are grafted by polymer chains of N monomers immersed in a chemically identical polymer melt of polymerization index P. The calculation shows that, for big particles (R_p ? N^1/2a, with a the segment size), the interactions and density profiles of the grafted layers are that of brushes at flat interface; While for small particles (R_p ? N^1/2a), the interactions and density profiles are characteristic of star polymers. In the case of intermediate grafted chain lengths, that is, R_p ～ N^1/2a, we found that the grafting density of the polymers and the radius of the spherical nanoparticles are both important in determining the structure and interactions of the grafted layers. Our findings suggest possible ways to tailor the structure and interactions of the nanoparticles to benefit the fabrication of polymeric nanocomposites. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2811–2820, 2006     

Gas permeability and n‐butane solubility of poly(1‐trimethylgermyl‐1‐propyne)

The gas permeability and n‐butane solubility in glassy poly(1‐trimethylgermyl‐1‐propyne) (PTMGP) are reported. As synthesized, the PTMGP product contains two fractions: (1) one that is insoluble in toluene and soluble only in carbon disulfide (the toluene‐insoluble polymer) and (2) one that is soluble in both toluene and carbon disulfide (the toluene‐soluble polymer). In as‐cast films, the gas permeability and n‐butane solubility are higher in films prepared from the toluene‐soluble polymer (particularly in those films cast from toluene) than in films prepared from the toluene‐insoluble polymer and increase to a maximum in both fractions after methanol conditioning. For example, in as‐cast films prepared from carbon disulfide, the oxygen permeability at 35 °C is 330 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 73 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. After these films are conditioned in methanol, the oxygen permeability increases to 5200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 6200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. The rankings of the fractional free volume and nonequilibrium excess free volume in the various PTMGP films are consistent with the measured gas permeability and n‐butane solubility values. Methanol conditioning increases gas permeability and n‐butane solubility of as‐cast PTMGP films, regardless of the polymer fraction type and casting solvent used, and minimizes the permeability and solubility differences between the various films (i.e., the permeability and solubility values of all conditioned PTMGP films are similar). © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2228–2236, 2002     

Investigation of polymer–solvent interactions in poly(styrene sulfonate) thin films

The swelling behavior of acid form poly(styrene sulfonate) (PSS‐H) thin films were investigated using in situ spectroscopic ellipsometry (SE) to probe the polymer–solvent interactions of ion‐containing polymers under interfacial confinement. The interaction parameter (χ), related to the polymer and solvent solubility parameters in the Flory–Huggins theory, describes the polymer‐solvent compatibility. In situ SE was used to measure the degree of polymer swelling in various solvent vapor environments, to determine χ for the solvent‐PSS‐H system. The calculated solubility parameter of 40–44 MPa^1/2 for PSS‐H was determined through measured χ values in water, methanol, and formamide environments at a solvent vapor activity of 0.95. Flory–Huggins theory was applied to describe the thickness‐dependent swelling of PSS‐H and to quantify the water‐PSS‐H interactions. Confinement had a significant influence on polymer swelling at low water vapor activities expressed as an increased χ between the water and polymer with decreasing film thickness. As the volume fraction of water approached ～0.3, the measured χ value was ～0.65, indicating the water interacted with the polymer in a similar manner, regardless of thicknesses. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1365–1372     

Comment on the concentration and temperature dependences of the translational diffusion coefficient of flexible-coil macromolecules in solution: Poly(2-vinyl pyridine) in tetrahydrofuran

Concentration-dependence coefficients k_D^? of the mutual diffusion coefficient of poly(2-vinyl pyridine) in tetrahydrofuran in the temperature range 15–55°C are compared with predictions of recent theories of macromolecular diffusion. In this temperature range a change in local conformation of the polymer occurs. The accompanying changes in chain solvation and coil hydrodynamics result in a sizable decrease in the hydrodynamic interaction parameter X defined by Akcasu. The formulation of theory appropriate for comparison with frame-indifferent experimental diffusivities is discussed. We find that current theories predict qualitatively, but not quantitatively, the change in temperature dependence of k_D^? that occurs at the conformational transition. The discrepancies closely parallel those reported in recent independent comparisons of theoretical k_D^? versus experimental data for flexible-coil molecules. No theory can adequately predict k_D^? over a wide range of X.     

Phase separation of poly(γ-benzyl L-glutamate) to liquid crystal and isotropic solution in various helicogenic solvents

Solvent effects on the phase separation of poly(-benzyl L-glutamate) to liquid crystal and isotropic solution have been observed in various helicogenic solvents. The temperature-composition phase diagrams have been determined for each solution. The critical concentrations, ₂ ^* , at which the phase separation occours have been compared in various solvents. In dimethylformamide in which the polymer is molecularly dispersed, the observed ₂ ^* value has agreed with that calculated by Flory's theory. In some solvents in which the polymer aggregates in a head-to-tail mode such as chloroform, the observed ₂ ^* values have been considerably small. It is assumed that the polymer aggregates behave as longer particles than the original particles. In dioxane in which the polymer aggregates highly both in a head-to-tail and a side-by-side modes, the ₂ ^* value has been a little larger than that in chloroform. In this case the relationship between the aggregation and the liquid crystal formation is so complicated that further investigation is necessary. In aromatic solvents such asm-cresol that dissolves the polymer almost molecularly, the ₂ ^* is smaller than that in dimethylformamide. Therefore, the intermolecular interactions between the phenyl groups in the side groups of the polymer and those in solvent molecules must be considered.The author is grateful to Mr. K. Sano and Mr. M. Watanabe for their observation of the liquid crystal formation.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

Determination of Polymer Compatibility by Viscometric Measurements on Ternary Solutions of the Two Polymers

Results on the intrinsic viscosity [η] are reported for the system solvent(1)/polymer(2)/polymer(3) in which the solvent was benzene, polymer(2) was polystyrene (PS), and polymer(3) was poly(dimethylsiloxane) PDMS. The values of [η] were then used to determine the likely compatibility of polymer blends of PS and PDMS. Initial focus was on the traditional interaction parameter b ₂₃ ⁽¹⁾ used by several authors to predict compatibilities, it but depends on the molar mass, weight fractions, and concentrations of each polymer. A new interaction parameter b ₂₃ ⁽²⁾ that is independent of polymer(3) concentration and molar mass was evaluated for determinations of polymer compatibility.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

Novel triarylamine‐based alternating conjugated polymer with high hole mobility: Synthesis,electro‐optical,and electronic properties

Novel bi‐triphenylamine‐containing aromatic dibromide M3 , N,N‐bis(4‐bromophenyl)‐N′,N′‐dipheny‐l,4‐phenylenediamine, was successfully synthesized. The novel conjugated polymer P1 having number‐average molecular weight of 1.31 × 10⁴ was prepared via Suzuki coupling from the dibromide M3 and 9,9‐dioctylfluorene‐2,7‐diboronic acid bis(1,3‐propanediol) ester. Polymer P1 had excellent thermal stability associated with a high glass‐transition temperature (T_g = 141 °C). The hole‐transporting and UV‐vis‐near‐infrared electrochromic properties were examined by electrochemical and spectroelectrochemical methods. Cyclic voltammograms of the conjugated polymer films cast onto indium‐tin oxide‐coated glass substrates exhibited two reversible oxidation redox couples at E_1/2 values of 0.73 and 1.13 V versus Ag/Ag⁺ in acetonitrile solution. The hole mobility of the conjugated polymer P1 revealed ～10^?3 cm² V^?1 s^?1, which is much higher than that of other conjugated polymer systems. The observed UV‐vis‐near‐infrared absorption change in the conjugated polymer film P1 at applied potentials ranging from 0.00 to 1.23 V are fully reversible and associated with strong color changes from pale yellowish in its neutral form to green and blue in its oxidized form. Using a combination of experimental study and theoretical investigation, we proposed an oxidation mechanism based on molecular orbital theory, which explains the cyclic voltammetry experimental results well. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Liquid–liquid phase separation in multicomponent polymer solutions. IX. Concentration-dependent pair interaction parameter from critical miscibility data on the system polystyrene–cyclohexane

Critical miscibility data obtained from measurements of phase-volume ratios have been used to calculate the concentration dependence of the pair interaction parameter for the system polystyrene–cyclohexane. The measured temperature and concentration ranges are 11–30°C and 4–18% polymer by weight, respectively. With the Gibbs free energy of mixing expressed in polymer segment mole fractions, x^*, the pair interaction parameter is g(x^*, T) = 0.4961 + 71.92/T + 0.2312x^* + 0.0750x^*2. In a polymer volume fraction formulation the parameter is g(φ, T) = 0.4099 + 90.65/T + 0.2064 φ + 0.0518 φ², which approximates to χ(φ, T) = 0.2035 + 90.65/T + 0.3092 φ + 0.1554 φ². Comparison of the temperature and concentration dependence with that obtained by other authors shows very good agreement, even when extensive extrapolations in temperature and concentration are applied. The present function is believed to be the most accurate. Solutions of mixtures of two narrow-distribution polystyrenes in cyclohexane show separation into three liquid phases under the exact conditions predicted by theoretical calculation with the present pair-interaction function.     

Swelling of polyacrylamide gels in polyacrylamide solutions

Swelling behavior of polyacrylamide (PAAm) and polyacrylamide-co-polyacrylic acid (PAAm-co-PAAc) gels was investigated in aqueous solutions of monodisperse PAAms with molecular weights (M_w) ranging from 1.5 × 10³ to 5 × 10⁶ g/mol. The volume of the gels decreases as the PAAm concentration in the external solution increases. This decrease becomes more pronounced as the molecular weight of PAAm increases. The classical Flory–Huggins (FH) theory correctly predicts the swelling behavior of nonionic PAAm gels in PAAm solutions. The polymer–polymer interaction parameter χ₂₃ was found to decrease as the molecular weight of PAAm increases. The swelling behavior of PAAm-co-PAAc gels in PAAm solutions deviates from the predictions of the FH theory. This is probably due to the change of the ionization degree of AAc units depending on the polymer concentration in the external solution. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1313–1320, 1998     

Topologically entangled polymers

Summary The statistical mechanics of a ring polymer confined to a plane and entangled with many randomly placed thin rods perpendicular to the plane are considered. The entanglements are characterized by the Gauss linking number. If the statistics of the random distribution of the rods is given by only the second cumulant then it is shown that the resulting entanglement problem can be solved formally exactly. For this special case the exact solution becomes possible because the problem can be reduced to one involving the winding of the polymer around one infinitely thin rod. The exact solution can be obtained for both the annealed and the quenched random distribution of obstacles. The entanglement of the ring polymer around the obstacles leads to a repulsive topological potential which is an effective interaction between the polymer and the rods. The origin of this potential is solely due to the constraint that the winding number be conserved. It is shown that forR ²/Lll (R is the location of the polymer segment,L is the total length of the polymer, andl is the length of the monomer) the topological potential for the annealed random case goes asN ln ln(Ll/R ²) whereN is the number of obstacles whereas for the quenched random case the potential is given byC lnLl/R ², whereC is a numerical constant that depends onN.     

Conformation of poly(dimethyl siloxane) and polystyrene in solution measured by polarized Raman scattering

Depolarization ratios ρ have been measured over ranges of temperature T and molecular weight M for polystyrene (PS) dissolved in cyclohexane (1002 cm^?1 Raman band) and for poly(dimethyl siloxane) (PDMS) dissolved in benzene (2907 cm^?1 Raman band). The ranges in the case of PS are 15 < T < 65°C and 2 × 10³ < M < 4 × 10⁵ and in the case of PDMS are ?3 < T < 60°C and M = 10⁴. Measurements were also made of PDMS radii of gyration using conventional light scattering. The results are interpreted in terms of a theory connecting rotational isomeric populations with polymer extension. In the case of PDMS, an experimental value of the proportionality constant for trans isomers (D₂ = ?3.9 ± 0.9) is deduced. This is closer to the theoretical value than previous estimates but there is still some discrepancy. In the case of PS the isomeric changes resulting from extension are independent of M for M > 10⁴. Deviations are observed for lower M.