Platinum(II) complexes containing 2-(alkenyl)pyridines

The ligands 2-(allyl)pyridine(APy), and 2-(1-methallyl)pyridine (1-MAPy) react with [Pt₂X₄(PEt₃)₂] (X = Cl or Br), in acetone solution to give complexes of the type [PtX(PEt₃)L] [PtX₃(PEt₃)], (L = APy or 1-MAPy), which contain a bidentate 2-(alkenyl)pyridine, whereas the same reaction in benzene solution gives trans-[PtBr₂(PEt₃)L], (L = APy or 1-MAPy), which contains a monodentate 2-(alkenyl)pyridine; ¹H NMR spectra indicate that both types of product undergo olefin exchange in solution. The same reaction with 2-(3-methallyl)-pyridine [2-(2-butenyl)pyridine] (3-MAPy), 2-(3,3-dimethylallyl)pyridine [2-(3-methyl-2-butenyl)pyridine] (3,3-DMAPy), and 2-(3-butenyl)pyridine (BPy), in either acetone or benzene solution, gives only trans-[PtBr₂(PEt₃)L]. The reaction of trans-[PtBr₂(PEt₃)L] (L = APy or 3-MAPy) with AgClO₄ gives [PtBr(PEt₃)L]ClO₄. Complexes of the type [PtCl₂L], which contain bidentate 2-(alkenyl)pyridines, result on reaction of L = APy, 3-MAPy, 3,3-DMAPy, BPy, MBPy with [Pt₂Cl₄(C₂H₄)₂].     

Controlled polymerization of acrylic acid under 60Co irradiation in the presence of dibenzyl trithiocarbonate

The polymerization of acrylic acid (AA) was performed under ⁶⁰Co irradiation in the presence of dibenzyl trithiocarbonate at room temperature, and well‐defined poly(acrylic acid) (PAA) with a low polydispersity index was successfully prepared. The gel permeation chromatographic and ¹H NMR data showed that this polymerization displays living free‐radical polymerization characteristics: a narrow molecular weight distribution (M_w/M_n = 1.07–1.22), controlled molecular weight, and constant chain‐radical concentration during the polymerization. Using PAA? S? C(?S)? S? PAA as an initiator, the extension reaction of PAA with fresh AA was carried out under ⁶⁰Co irradiation, and the results indicated that this extension polymerization displayed controlled polymerization behavior. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3934–3939, 2001     

Synthesis of polyester and copolyesters having amino acid moieties in the main chain

N, N-di (2-hydroxyethyl)-3-aminopropionic acid (M3) was synthesized and used for the preparation of a series of polyesters having amino acid moieties in the main chain and carboxyl groups as the side group. Polycondensation of M3 , diols, bisphenol A, and isophthaloyl dichloride were performed in the presence of tertiary amine by solution and interfacial methods. Molecular weights of the polymers obtained by the solution method were not high, because oligomers produced at the early stage of reaction are ionized by H⁺ ions from the by-product, and become nonreactive triethylamine hydrochloride. Polymers with high M?_w (1–10 × 10⁴) were obtained in a high yield by organic/organic two-phase interfacial polycondensation using DMAc and n-heptane as solvents. The combined nucleophilic and basic complex catalytic action of N, N, N′, N′-tetramethyl ethyiene diamine (TEMED) is suggested for the present organic phase/organic phase interfacial polycondensation. This method can be applied for the preparation of novel functional polyesters. © 1994 John Wiley & Sons, Inc.     

Preparation and some properties of nylon 46

Nylon 46 was synthesized from the salt of 1,4-diaminobutane and adipic acid. High molecular weight polymers could be obtained by reaction for 1 hr at 215°C in a closed system and at least for 1 hr in vacuo at a temperature in the range 290–305°C. The reactions at 290°C were found to have taken place in the solid state and those at 305°C in the melt. The highest molecular weights (M?_w ca. 45,000) were obtained by reaction at 290°C with a nylon salt with a pH of 7.8–8.0. The molecular weight characteristics were studied with end-group analysis, viscometry, light scattering, and ultracentrifugation. The polymers were found to be gel-free and monodisperse (M?_w/M?_n ～ 1.15). Films could be cast from formic acid. From x-ray diffraction patterns, measured on such films, spacings of 3.74 and 4.30 Å were calculated, whereas a long period of 66 Å was also found. The infrared spectra showed all the usual amide bands of even–even polyamides. The melting temperature was found to vary between 283 and 319°C, depending on the thermal history of the sample. Water absorption measured on a cast film showed this to be very hygroscopic (7.5% at 65% RH), while a highly crystalline sample absorbed only little water (1.6% at 65% RH).     

Aromatic poly(amic acids): Fundamental structural studies

Aromatic poly(amic acids) derived from pyromellitic dianhydride and 4,4′,-diaminodiphenyl ether were characterized by dilute solution techniques. Number-average molecular weights M?_n of 13 samples ranged from 13,000 to 55,000 (DP 31–131). Weight-average molecular weights M?_w of 21 samples ranged from 9,900 to 266,000. The ratio M?_w/M?_n was between 2.2 and 4.8. Heterogeneous polymerization yielded higher molecular weight polymer than homogeneous polymerization. The molecular weight could be varied systematically by control of stoichiometric imbalance. Use of very pure monomers and solvent gave polymers of relatively high number-average molecular weight (～50, 000) and the most probable molecular weight distribution M?_w/M?_n = 2. Impure monomers and/or solvent resulted in lower number-average molecular weight (M?_n ? 20,000–30,000) and wider distributions (M?_w/M?_n = 3–5). The Mark-Houwink relation obtained was [η] = 1.85 × 10^?4M?_w^0.80 The exponent is characteristic of moderately extended solvated coils. The unperturbed chain dimensions (r₀² /M)^1/2 were 0.848 A., and the steric factor σ was 1.24 which is close to the limiting value of unity for an equivalent chain with free internal rotations. The sedimentation constant–molecular weight relation was S₀ = 2.70 × 10^?2M?_w^0.39. This exponent is consistent with the Mark-Houwink exponent.     

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

<Superscript>1</Superscript>H NMR study on microstructure of a novel acrylamide/methacrylic acid template copolymer in aqueous solution

A novel acrylamide/methacrylic acid template copolymer was prepared using polyallylammonium chloride (PAAC) as a template. This copolymer contains acrylamide (PAM), phenoxy acrylate (POA), and acylic acid (PAA) blocks. The investigation by high resolution nuclear magnetic resonance (¹H NMR) shows that intramolecular hydrogen bonds between the PAM and PAA blocks lead to compact molecular arrangement at quite low pH values, and the motion of the phenoxy side chain of the POA blocks is somewhat restricted. With the increase in pH value of the solution, the carboxylic acid of the PAA block gradually dissociates, which weakens hydrogen bonds between the PAM and PAA blocks. The decrease in D _w, self-diffusion coefficient of water, indicates the growth in aggregate size of the template copolymer. The cross peaks between amide protons and backbone protons shown in 2D nuclear overhauser spectroscopy (NOESY) spectra imply the existence of the intermolecular hydrogen bonding interaction between PAM and PAA blocks. After the carboxylic acid of the PAA block is completely dissociated in alkaline solution, the electrostatic repulsion of the carboxylic ion makes the molecular chain of the copolymer exhibit more outstretched. Consequently, the phenoxy groups (the side chain of the POA block) have more space to move.     

The drawing behavior of linear polyethylene. I. Rate of drawing as a function of polymer molecular weight and initial thermal treatment

The drawing behavior of a series of linear polyethylene homopolymers with weight-average molecular weight (M?_w) ranging from 67,800 to ～3,500,000 and variable distribution (M?_w/M?_n = 5.1?20.9) has been studied. Sheets were prepared by two distinct routes: either by quenching the molten polymer into cold water or by slow cooling below the crystallization temperature (～120°C) followed by quenching into cold water. When the samples (2 cm long) were drawn in air at 75°C using a crosshead speed of 10 cm/min it was found that for low M?_w polymers the initial thermal treatment has a dramatic effect on the rate at which the local deformation proceeds in the necked region. At high M?_w such effects are negligible. An important result was that comparatively high draw ratios (λ > 17) and correspondingly high Young's moduli could be obtained for a polymer with M?_w as high as 312,000. It is shown how some of the structural features of the initial materials (mainly studied by optical microscopy, small-angle x-ray scattering and low-frequency laser Raman spectroscopy) can be interpreted in terms of the molecular weight and molecular weight distribution of the polymers. Although crystallization and morphology can be important at low M?_w, it suggested that the concept of a molecular network which embraces both crystalline and noncrystalline material is more helpful in understanding the drawing behavior over the whole range of molecular weights.     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Living cationic polymerization of 2-vinyloxyethyl phthalimide: Synthesis of poly(vinyl ether) with pendant primary amino functions

Cationic polymerization of 2-vinyloxyethyl phthalimide ( 1 ) in CH₂Cl₂ at ?15°C with hydrogen iodide/iodine (HI/I₂) as initiator led to living polymers of a narrow molecular weight distribution (M?_w/M?_n = 1.1–1.25). The number-average molecular weight of the polymers was in direct proportion to monomer conversion and could be controlled in the range of 1000–6000 by regulating the 1 /HI feed ratio. However, when a fresh monomer was supplied to the completely polymerized reaction mixture, the molecular weight of the polymers was not directly proportional to monomer conversion. The polymerization of 1 by boron trifluoride etherate (BF₃OEt₂) in CH₂Cl₂ at ?78°C gave polymers with relatively high molecular weight (M?_w > 20,000) and broad molecular weight distribution (M?_w/M?_n ～ 2). The HI/I₂-initiated polymerization of 1 was an order of magnitude slower than that of ethyl vinyl ether, probably because of the electron-withdrawing phthalimide pendant. Hydrazinolysis of the imide functions in poly( 1 ) gave a water-soluble poly(vinyl ether) ( 3 ) with aliphatic primary amino pendants.     

Fundamental studies on cationic polymerizations: Molecular weights and molecular weight distributions of polyisobutylenes produced by γ-irradiation (free ions) and chemical catalysis (ion pairs)

The molecular weights (M?_n, M?_v, and M?_w) and molecular weight distributions of polyisobutylenes synthesized by γ-irradiation in the range 29 to ?78°C have been determined. The plots of log M?_n, log M?_v, and log M?_w versus 1/T are linear and parallel (E_M? = ?6.3₆ ± 0.5), and M?_w/M?_n ≈ 3.0 ± 0.5 over this temperature range. The viscosity-average molecular weights of polyisobutylenes obtained by γ-irradiation were compared with those of polymers prepared by BF₃, EtAlCl₂, and AlCl₃. It is found that, at the same polymerization temperature, the M?_v of radiation-induced polyisobutylenes, which propagate by free carbonium ions, is significantly higher than those synthesized by the Lewis acids, which probably propagate via ion pairs. The implications of these findings are discussed, and it is concluded that the counterion in the proximity of the growing cation impedes propagation to a greater extent than it does the competing process of chain transfer to monomer.     

Effects of the thermal history and concentration on the aggregation of Erwinia gum in an aqueous solution

The aggregation of Erwinia (E) gum in a 0.2 M NaCl aqueous solution was investigated by multi‐angle laser light scattering and gel permeation chromatography (GPC) combined with light scattering. The GPC chromatograms of five fractions contained two peaks; the fractions had the same elution volume but different peak areas, suggesting that aggregates and single chains coexisted in the solution at 25 °C. The apparent weight‐average molecular weights (M_w) of the aggregates and single chains for each fraction were all about 2.1 × 10⁶ and 7.8 × 10⁴, respectively. This indicates that the aggregates were composed of about 27 molecules of E gum in the concentration range used (1.0 × 10⁻⁶ to 5.0 × 10⁻⁴ g/mL). The weight fraction of the aggregates (w_ag) increased with increasing concentration, but the aggregates still existed even in an extremely dilute solution. The fractionation process and polymer concentration hardly affected the apparent aggregation number but significantly changed w_ag. The E‐gum M_w decreased sharply with an increase in temperature. When the E‐gum solution was kept at 100 °C, w_ag decreased sharply for 20 h and leveled off after 100 h. Once the aggregates were decomposed at a higher temperature, no aggregation was observed in the solution at 25 °C, indicating that the aggregation was irreversible. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1352–1358, 2000     

The effect of temperature and solvent on the synthesis and properties of nylon 610 made from sebacyl bisketene

Polyamides were synthesized at ?60°, ?40°, ?20°, and 0°C from sebacyl bisketene and 1,6-hexamethylenediamine in either acetone or methylene chloride. At the lower reaction temperatures oligomers predominated in solution but at 0°C the product was crosslinked. The polyamides were subjected to m-cresol extraction at elevated temperatures for up to 14 days. The m-cresol soluble and insoluble fractions were characterized by weight, infrared spectroscopy, dilute solution viscosity, and gel permeation chromatography. Infrared analysis of the soluble and insoluble portions showed the degree of branching of the polyamide, identified the branching point at the secondary amide proton position, and gave an indication of the degree of branching required before insoluble products resulted. Dilute solution viscosity and gel permeation chromatography were used to demonstrate the existence of low molecular weight (M_w) oligomer species in the soluble portion. Differential scanning calorimetry experiments revealed that polyamides synthesized below their glass transition temperature would not crystallize which resulted in abnormal thermal characteristics. Annealing at elevated temperatures allowed crystallization to occur and the expected thermal character to develop.     

Effect of temperature and molecular weight on the rate of spreading of polystyrene melts on plane soda lime glass surfaces

The effect of temperature T and weight-average molecular weight M?_w on the rate of spreading of polystyrene melts on plane solid surfaces has been examined. The activation energy E of spreading was estimated to be 25.2 ± 3 kcal/mole, which is of the same magnitude as the activation energy for flow of polystyrene melts. The rate of spreading was found to be inversely proportional to M?_w raised to the 1.5 power. This rate of spreading, measured as the time rate of increase in the liquid–solid contact area, dA/dt, could be expressed as where γ_1v is the melt surface tension and θ_d and θ_s are the dynamic and static contact angles, respectively. The numerical value of K has been calculated to be (6.025 ± 3.693) × 10^?14 in the temperature range of 110–260°C and for the values of M?_w from 2000 to 37000.     

Direct polycondensation of aromatic dicarboxylic acids and bisphenols with tosyl chloride and N,N-dimethylformamide in pyridine

A Vilsmeier adduct derived from arylsulfonyl chlorides and DMF in pyridine was successfully used as a new condensating agent for the synthesis of aromatic polyesters by the direct polycondensation of aromatic dicarboxylic acids and bisphenols and also of hydroxybenzoic acids. Polymers of high molecular weights (M?_w = 78,000) with relatively narrow molecular weight distribution (M?_w/M?_n ≈ 3.0) were prepared by reacting aromatic dicarboxylic acids with the adduct in pyridine, followed by addition of bisphenols. The polycondensation was significantly affected by the amount of DMF, the nature of the arylsulfonyl chlorides, the conditions of initial reaction of the acids with the adduct, and the rate of reaction with bisphenols. The process was adaptable to the direct polycondensation of hydroxybenzoic acids, affording polymers of high molecular weight (η_inh = 1.73).     

Synthesis and properties of poly(hydroxyurethane)s

Bis(cyclic Carbonate)s 1 were prepared by the reaction of bis(epoxide)s and atmospheric pressure of CO₂ in the presence of sodium iodide and triphenylphosphine as catalysts at 100°C in high yield. Polyaddition of 1 and hexamethylenediamine ( 2a ) or dodecamethylenediamine ( 2b ) in dimethylsulfoxide or N,N-dimethylacetamide (DMAc) at 70 or 100°C for 24 h afforded corresponding poly(hydroxyurethane)s with M?_n 20,000–30,000. When ethylenediamine ( 2c ) or 1,3-propanediamine ( 2d ) was used as a diamine, poly(hydroxyurethane)s with lower molecular weight were obtained. The presence of water, methanol, or ethyl acetate in the solvent had little effect on the M?_n of the polymer obtained, because of the high chemoselectivity of the reaction of the five-membered cyclic carbonate and amine. Polyaddition of bis(cyclic carbonate) bearing ester groups and 2a also afforded the corresponding poly(hydroxyurethane) without aminolysis of the ester groups. Poly(hydroxyurethane) 3 obtained from the bis(cyclic carbonate) derived from bisphenol A was less soluble in organic solvents than model polyurethane 8 having no hydroxy groups obtained from 4,4′-isopropylidenebis(2-hydroxyethoxybenzene) and hexamethylene diisocyanate, and was thermally stable as well as 8.3 easily undertook crosslinking at room temperature by the treatment with hexamethylene diisocyanate or aluminium triisopropoxide in DMAc or tetrahydrofuran. The gel crosslinked by aluminium triisopropoxide regenerated the original polymer at room temperature by treatment with 1.5 equiv of 1.2M HCl in N-methylpyrollidinone for 1 h. © 1993 John Wiley & Sons, Inc.     

Structural transitions of nanocrystalline domains in regioregular poly(3‐hexyl thiophene) thin films

The effects of solution processing and thermal annealing on thin film morphology and crystalline structures of regioregular poly(3‐hexyl thiophene) (RR P3HT) are studied in terms of molecular weight (M_w). Using grazing‐incidence X‐ray diffraction, π‐conjugated planes in drop‐cast films from chloroform solutions are found to be preferentially oriented parallel to the substrates regardless of M_w. However, the mesoscale nanocrystalline morphology of the drop‐cast films is significantly affected by M_w, exhibiting a distinctive morphological transition from short nanorods to long nanofibrils above a critical number‐averaged M_w (～ 3.6 kDa). This is probably due to the change in a conformation change from an extended‐chain to a folded‐chain, as M_w of RR P3HT increases. In contrast, spin‐casting of high M_w RR P3HT produces less ordered films with a lower crystallinity and mixed parallel/perpendicular orientations of π‐conjugated planes. The crystallinity and parallel π‐conjugated orientation of RR P3HT in spin‐cast films could be improved by thermal treatments at high‐temperatures either (1) above the glass transition temperature or (2) above the melting temperature of RR 3PHT followed by recrystallization upon cooling under vacuum. However, the charge mobility of the spin‐cast films for a field‐effect transistor application is still lower than that of the drop‐cast films. This would be attributed to the chain oxidation and the development of distinct grain boundaries between RR P3HT nanofibrils during the thermal treatments. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1303–1312, 2007     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Preparation,characterization and thermal degradation study of poly(amide imide)s based on tri-component mixture of PMDA/BTDA,diamines and acid chloride

A series of poly(amide imide)s (PAIs) having alternate (amide–amide) and (imide–imide) units (polymers 1–14 and 22–35), and random distribution of amide-imide linkages (polymers 15–21 and 36–42) were prepared by low temperature solution polymerization of benzene-1,2,4,5-tetracarboxylic dianhydride (PMDA)/benzophenone-3,3′,4,4′-tetracarboxylic dianhydride (BTDA), diamines (cyclic and aromatic) and acid chloride in dimethylforamide. All the polymers were readily soluble in polar aprotic solvents with inherent viscosities in the range of 0.134–0.878. The process of cycloimidization of poly(amide amic acid)s (PAAs) to PAIs was investigated by TGA and FT-IR techniques at four different temperatures i.e., 175, 200, 225, and 260 °C. The rate of cycloimidization was calculated by taking into account the theoretical weight loss (W_T), obtained from [n × M_w (H₂O)/M_w (R_U)] W, where M_w (H₂O) molecular weight of water, W weight of PAA taken for TGA, M_w (R_U) the molecular weight of repeat unit of PAA, n number of water molecules eliminated per repeat unit of PAA upon cycloimidization. For a particular diamine, the extent of percentage cycloimidization at the end of the isothermal heating was higher for PAAs containing trimellitic anhydride chloride (TMAc) unit, irrespective of the nature of the dianhydride and diamine. Thermal and thermooxidative degradation of PAIs was investigated by TGA in nitrogen and oxygen atmosphere. The initial decomposition temperatures (IDT) of polymers are above 260 °C, and vary widely (from 260 to 501 °C) depending upon the structure of the polymer backbone. PAIs containing TMAc exhibited higher thermal stability as compared to those polymers having diacid chloride units, in both N₂/O₂ atmospheres.     

Multimerization: Association and aggregation. XIII. Concentration dependence of apparent average molecular weights of a poly-disperse associating polymer in a theta solvent

Analytical expressions are derived for the concentration dependences of different apparent average (n,w,z) molecular weights for two types (end-to-end and segment-to-segment) of open association of polymolecular unimers. The open association is defined as an association leading to an unlimited number of multimer species. The type of association depends upon the number of associogenic sites per unimer molecule: for the end-to-end type this number is constant, whereas for the segment-to-segment type it is proportional to the degree of polymerization of the unimer. For the end-to-end association, a simple relation exists between the polydispersity (M?_r)_w/(M?_r)_n of the mul-timer and the association number r and the polymolecularity (M?_I)_w/(M?_I)_n of the unimers: (M?_r)_w/(M?_r)_n = 1 + r^?1[(M?_I)_w/(M?_I)_n ? 1]. The z-average and higher averages of the r-mers may be lower than the corresponding averages of the unimers. In the theta-state, (M?_n)_app,Θ and (M?_w)_app,Θ are linear functions of c/(M?_n)_app,Θ, whereas a more complicated relation exists for the apparent higher averages. For the segment-to-segment association, both (M?_w)_app,Θ and (M?_z)_app,Θ are linear function of the weight concentration c, whereas no closed expression could be found for (M?_n)_app,Θ. For the polydispersities of multimers one finds (M?_I)_z/(M?_r)_w = 1 + r^?1[(M?_I)_z/(M?_I)_w ? 1], and, in the special case of a Schulz-Zimm distribution of unimer molecular weights, (M?_r)_n/(M?_r)_w = 1 + r^?1[(M?_I)_n/(M?_I)_w ? 1].