Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

Intrinsic viscosity in branched free-radical polymers

The intrinsic viscosity ratio [η]_B/[η]_L was calculated as a function of average branching density for trifunctionally branched, free-radical polymers. Calculations were made for the g^1/2, g^3/2, and h³ rules, using realistic distributions of molecular weights and branches. Experimental data on branched poly(vinyl acetate) lay between the curves obtained from the g^1/2 and h³ relations.     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Combination of nitroxide‐mediated polymerization and SET‐LRP for the synthesis of high molar mass branched and star‐branched poly(n‐butyl acrylate) characterized by size exclusion chromatography and rheology

Branched and star‐branched polymers were successfully synthesized by the combination of two successive controlled radical polymerization methods. A series of linear and star poly(n‐butyl acrylate)‐co‐poly(2‐(2‐bromoisobutyryloxy) ethyl acrylate) statistical copolymers, P(nBA‐co‐BIEA)_x, were first synthesized by nitroxide‐mediated polymerization (NMP at T > 100 °C). The subsequent polymerization of n‐butyl acrylate by single electron transfer‐living radical polymerization (SET‐LRP at T = 25 °C), initiated from the brominated sites of the P(nBA‐co‐BIEA)_x copolymer, produced branched or star‐branched poly(n‐butyl acrylate) (PnBA). Both types of polymerizations (NMP and SET‐LRP) exhibited features of a controlled polymerization with linear evolutions of logarithmic conversion versus time and number‐average molar masses versus conversion for final M_n superior to 80,000 g mol^?1. The branched and star‐branched architectures with high molar mass and low number of branches were fully characterized by size exclusion chromatography. The Mark–Houwink Sakurada relationship and the analysis of the contraction factor (g′ = ([η]_branched/[η]_linear)_M) confirmed the elaboration of complex PnBA. The zero‐shear viscosities of the linear, star‐shaped, branched, and star‐branched polymers were compared. The modeling of the rheological properties confirmed the synthesis of the branched architectures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Application of gel permeation chromatography and viscometry for characterization of branched polydisperse polycarbonate

Gel permeation chromatography (GPC) and viscometry (V) methods have been combined for determination of long-chain branching in bisphenol-A polycarbonate (PC) by means of a branching factor $\text{g}{}_{\mathrm{v}}\text{=}\text{M}{}_{\mathrm{vg}}{}^1\text{/}\text{M}{}_{\mathrm{v}}{}^1$, where $\text{M}{}_{\mathrm{vg}}{}^1$ and $\text{M}{}_{\mathrm{v}}{}^1$ are the apparent viscosity-average molecular weights calculated from GPC data and from intrinsic viscosities [η] of the samples respectively. A linear dependence of g_v on molar % of branching agent has been obtained. The GPC data on PC samples have also been applied for verification of an earlier [η]?M relationship for branched polydisperse polymers.     

Intrinsic viscosities of four homopolymers and one copolymer in nonpolar solvents. I. Effect of correlations of molecular orientations

Intrinsic viscosities [η] of four homopolymers, polyisobutylene (PIB), polypentene-1 (PP-1), polypentenamer (PPmer), and polydimethylsiloxane (PDMS), and of an ethylene-propylene copolymer containing 81% ethylene (81% E) have been measured at 25°C in seven linear alkanes ranging from n-C₆ to n-C₁₆ and three highly branched alkanes, 2,2,4-trimethylpentane, 2,2,4,6,6-pentamethylheptane, and 2,2,4,4,6,8,8-heptamethylnonane. Correlation of molecular orientations (CMO) in the polymers was investigated. The difference Δ[η] = [η](lin) ? [η](br) is used as a test of CMO with the supporting assumption that CMO lowers the free energy and the destruction of CMO raises it. The positive value of Δ[η], which varies from 20% to 40% for PPmer and 81% E, is indicative of orientational order in these two polymers. The negative value of Δ[η] for PDMS results from the disordering of linear alkanes by the nonordered PDMS. δ[η] is near zero for PP-1 and small for PIB implying that these two polymers are indifferent to solvent molecular shape. The variation of [η] with alkane chain length of the linear alkanes gives additional information about size and solvent quality. The dependence is small for ordered polymers due to the short range of CMO. [η] diminishes rapidly with n for PDMS probably because of the increased difference of cohesive energy between polymer and solvent. The dependence is small for PIB but very large for PP-1. The much better quality of small-molecule solvents for PP-1 may be an indication of a helicoidal conformation of this polymer in solution.     

Evaluation of K⊖ from [η]-M-data of binary and ternary polymer systems

Unperturbed dimensions of flexible linear macromolecules can be obtained from [η]-M-data in any solvent, good or poor, single or mixed. Usually K_θ is estimated by a relationship between [η]/M_W^0.5 and M_w^0.5 first proposed by Burchard and by Stockmayer and Fixman. But, it is well-known that the Burchard-Stockmayer-Fixman-plot shows downward curvature, especially for good solvent systems. Various efforts have been made to achieve relations with better linearity. One of the first was the semi-empirical relation between ([η]/M_w^0.5)^0.5 and M_w/[η] by Berry. Predicting a relationship of the excluded volume parameter z to the viscosity expansion factor by α⁵_η instead of α⁵_η Tanaka obtains that ([η]/M_w^0.5)^5/3 is linear in M_w^0.5. By allowing for the dependence of the viscometric interaction parameter B, which is correlated to the second virial coefficient A₂, on molar mass, Gavara, Campos and Figueruelo predict a linear dependence of [η]/M_w^0.5 against A₂.M_w^0.5. It is not our intention here to discuss the validity of these theories, but to compare them with experimental data.     

Synthesis and solution properties of linear,four-branched,and six-branched star polyisoprenes

A number of linear, four- and six-branched regular star polyisoprenes were synthesized by anionic polymerization techniques in benzene using lithium as the counterion and polyfunctional silicon chloride compounds as the coupling agents. Light-scattering measurements in dioxane were performed in order to establish Θ solvent conditions. Determinations of the radius of gyration of the polymers of different structure indicate that g = 〈S²〉_0,br/〈S²〉_0,lin agree closely with random flight calculations for the ratios. Intrinsic viscosities determined in a Θ solvent establish g′ = [η]_br/[η]_lin to be 0.77₃ and 0.62₅ for the four- and six-branched polyisoprenes, respectively. In a good solvent g′ values are slightly lower. These values are compared with theoretical estimates. Viscosities of 19.29% (w/w) solutions of the polyisoprenes in n-decane at 25°C are correlated with the intrinsic viscosities of the polymers under Θ conditions.     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

Rigid rod-random coil transformation,Mark-Houwink constants,and Millich's intrinsic isoviscosity, [η]M,and isohydrodynamic volume, [η]MMM

On the basis of values of Mark–Houwink constants of rigid rod—polymer systems and their conformers a unique stage can be recognized which is common to all polymers of this type, independent of polymer conformation and solvent medium. The crude values derived for these polymer–solvent systems at 20–30°C. of Millich's intrinsic isoviscosity, [η]_M, is 0.28 ± 0.04 dl/g, occurring at the coordinate molecular weight, M_M, of 42,700, and produces a value of ca. 170 Å of Millich's isohydrodynamic polymer volume at this stage and temperature. Utility in the use of [η]_MM_M as a standard reference state, assuming reliable Mark–Houwink constants that obtain for strictly linear, monodisperse polymer samples, is indicated.     

The viscosities of dilute solutions of nitrocellulose

The viscosities of dilute solutions (0.05, 0.1, and 0.2 g. per 100 ml.) of relatively high nitrogen content nitrocelluloses, weight-average molecular weights ca. 100,000, have been studied using homologous series of methyl ketones, alkyl acetates, and dialkyl phthalates as solvents. The simple form of the Huggins equation, does not appear to hold, plots of η_sp/c against c being generally curved. The results are capable of expression by where A equals [η] and B the initial slope. Values of B and A appear to be related to solvent power as determined by the volume of hexane required to cause initial phase separation from solution, good solvents giving higher values of B and A than poor. The variation of B with solvent is more marked than that of [η] and may reflect differences in degree of coiling of chains in different solvents. Values of B/[η]² (Huggins k′) do not generally decrease with solvent power increase. The slopes of Martin plots divided by intrinsic viscosities are not generally related to solvent power in the manner observed by Spurlin with solutions of ethyl cellulose.     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Synthesis of Amphiphilic Azobenzene Functionalized Branched-Type Copolymer Based on Branched Poly(2-(Dimethylamino) ethyl methacrylate) and Investigation of Its Drug Release Properties

Here, we reported the synthesis of branched poly(2-(dimethylamino) ethyl methacrylate) (PDMAEMA) via a combination of activator generated by electron transfer atom transfer radical polymerization (AGET ATRP) and self-condensing vinyl polymerization (SCVP) techniques. The typical linear kinetics of the AGET ATRP of DMAEMA with the initiation of 2-(2-bromoisobutyryloxy) ethyl methacrylate (BIEM) was observed. The molecular weight (M_n ) of the branched PDMAEMA increased with the monomer conversion. The GPC traces of these polymers were unimodal and the molecular weight distributions (M_w/M_n ) were in the range of 1.30–2.10. The degree of branching (DB) determined by NMR spectra agreed with theoretical value. The branched amphiphilic copolymer functionalized with azobenzene was then prepared via AGET ATRP chain-extension of branched PDMAEMA with azobenzene monomer, 6-[4-(4-methoxyphenylazo)phenoxy]hexyl(meth)acrylate as the second monomer. The GPC traces of these branched copolymers showed the mono-peaks, which proved the successful preparation of copolymers. The properties of this branched copolymer in controlling drug release were also investigated. It was found that the drug release rate of chlorambucil can be controlled by various factors, such as polymer structure, light, temperature and pH values.     

Size Exclusion Chromatography of Polymers With Random Tetrafunctional Branching

Abstract

The behaviour of polydisperse branched copolymers of methyl methacrylate with a small amount of randomly situated tetrafunctional ethylenedimethacrylate units was investigated by means of size exclusion chromatography (SEC). A procedure has been suggested for the conversion of apparent values of molecular parameters of real polymer branched systems (M_{n, app}; M_{w, app} obtained from SEC data by calibration of the separation system using a linear polymer) into actual values. This was made possible by off-line coupling of SEC and viscometry. The branching was characterized by the weight average number of branching sites in the macro-molecule, m_w, and the branching index, y.     

Organometallic polymers I. Solution polymerization of α-ferrocenylmethylcarbonium fluoborate

The self-condensation of α-ferrocenylmethylcarbonium ion in nitroethane yielded polymers of M_n up to 20,000. The change of [η] and M_n with the reaction time indicated that the process consisted of a rapid primary growth stage, an induction period, a second growth stage, and a crosslinking stage. The [η]–M_n correlation for a series of polymeric fractions in the M_n = 0.1–7.2 × 10⁴ range points to a highly branched structure.     

pH‐Responsive ampholytic terpolymers of acrylamide,sodium 3‐acrylamido‐3‐methylbutanoate,and (3‐acrylamidopropyl)trimethylammonium chloride. I. Synthesis and characterization

Low-charge-density ampholytic terpolymers composed of acrylamide, sodium 3-acrylamido-3-methylbutanoate (NaAMB), and (3-acrylamidopropyl)trimethylammonium chloride were prepared via free-radical polymerization in 0.5 M NaCl to yield terpolymers with random charge distributions. NaOOCH was used as a chain-transfer agent during the polymerization to eliminate the effects of the monomer feed composition on the degree of polymerization (DP) and to suppress gel effects and broadening of the molecular weight distribution. The terpolymer compositions were obtained via ¹³C NMR spectroscopy, and the residual counterion content was determined via elemental analysis for Na⁺ and Cl⁻. The molecular weights (MWs) and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi-angle laser light scattering (SEC–MALLS); the terpolymer MWs ranged from 1.3–1.6 × 10⁶ g/mol, corresponding to DPs of 1.6–1.9 × 10⁴ repeat units, with all terpolymers exhibiting PDIs of less than 2.0. Intrinsic viscosities determined from SEC–MALLS data and the Flory–Fox relationship were compared to intrinsic viscosities determined via low-shear dilute-solution viscometry and were found to agree rather well. Data from the SEC–MALLS analysis were used to analyze the radius of gyration/molecular weight (R_g–M) relationships and the Mark–Houwink–Sakurada intrinsic viscosity/molecular weight ([η]–M) relationships for the terpolymers. The R_g–M and [η]–M relationships revealed that most of the terpolymers exhibited little or no excluded volume effects under size exclusion chromatography conditions. Potentiometric titration of terpolymer solutions in deionized water showed that the apparent pK_a value of the poly[acrylamide-co-sodium 3-acrylamido-3-methylbutanoate-co-(3-acrylamidopropyl)trimethylammonium chloride] terpolymers increased with increasing NaAMB content in the terpolymers and increasing ratios of anionic monomer to cationic monomer at a constant terpolymer charge density. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3236–3251, 2004     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Dilute solution properties of sodium amylopectin xanthate

Sodium amylopectin xanthate, prepared by xanthation of potato amylopectin in alkaline medium, was fractionated and the fractions in 1M NaOH were characterized by viscometry and light scattering. The expansion factor α was determined from the expression due to Orofino and Flory. The value of a of the Mark-Houwink relation, [η] = KM^a, was also determined. Its weight-average molecular weight, end-to-end distance, branching, and other parameters in alkali solution were also evaluated. From the data, it was concluded that the sodium amylopectin xanthate molecule had a polydisperse random-coil chain configuration in 1M NaOH and had no tendency to aggregate in this medium.