Effects of solvent goodness and polymer concentration on rejection of polystyrene from small pores

Solutions of polystyrene of molecular weight 4.5 × 10⁶ and 8.4 × 10⁶ in mixed solvents of carbon tetrachloride/methanol were filtered through track-etched mica membranes at low membrane velocities. The unperturbed hydrodynamic radius of the polymer was always larger than the pore radius. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was determined from material balances as a function of solvent flow rate per pore q, volume percent CCl₄ of the solvent, and polymer concentration C₀. In the dilute region (C₀ < C^*) σ was found to depend primarily on q and was essentially independent of chain size (or solvent goodness), molecular weight, and pore radius. In the semidilute region (C₀ > C^*) σ decreased significantly as C₀ was increased.     

Radical polymerization of methyl methacrylate in the presence of stereoregular poly(methyl methacrylate). V. Kinetics of initial template polymerization

The influence of stereoregular poly(methyl methacrylate) (PMMA) as a polymer matrix on the initial rate of radical polymerization of methyl methacrylate (MMA) has been measured between ?11 and +60°C using a dilatometric technique. Under proper conditions an increase in the relative initial rate of template polymerization with respect to a blank polymerization was observed. Viscometric studies showed that the observed effect could be related to the extent of complex formation between the polymer matrix and the growing chain radical. The initial rate was dependent on tacticity and molecular weight of the matrix polymer, solvent type and polymerization temperature. The accelerating effect was most pronounced (a fivefold increase in rate) at the lowest polymerization temperature with the highest molecular weight isotactic PMMA as a matrix in a solvent like dimethylformamide (DMF), which is known to be a good medium for complex formation between isotactic and syndiotactic PMMA. The acceleration of the polymerization below 25°C appeared to be accompanied by a large decrease in the overall energy and entropy of activation. It is suggested that the observed template effects are mainly due to the stereoselection in the propagation step (lower activation entropy Δ S_p^?) and the hindrance of segmental diffusion in the termination step (higher activation energy Δ E_t^?) of complexed growing chain radicals.     

Configurational effects on polystyrene rejection from microporous membranes

Dilute solutions of polystyrene in chloroform were filtered through track-etched mica membranes. The pores of each membrane were smaller than the mean unperturbed dimension of the polymer molecules. Three configurations of polystyrene were used: linear, comb-branched, and star-branched. The data for the linear polystyrenes show that the reflection coefficient σ decreases with solvent flow rate per pore q in a manner independent of molecular weight. At low flow rates the rejection is quantitatively described by 1 ? σ ～ q^1.69. Comparisons among the three configurations show that as the extent of branching increases, σ increases at given solvent flow rate. It is concluded that filtration studies with well-defined porous membranes can provide a relative measure of deformability among various configurations of polymeric species.     

Effect of chain length on rates of diffusion-limited small molecule-polymer and polymer-polymer reactions: Phosphorescence quenching studies

Model interactions have been studied by phosphorescence quenching to obtain a better understanding of the chain length dependence of interpolymeric chain end-chain end reactions such as those involved in the termination step of free radical polymerization. For small molecule-polymer interactions in dilute cyclohexane solution, quenching rate constant (k_q) data agree with the Smoluchowski equation prediction that k_q scales as polymer molecular weight (MW) to the -½ power, confirming self-diffusion control. For polymer-polymer interactions in dilute solution, the chain length dependence is weaker than that predicted by translational diffusion control, as described by the Smoluchowski equation, but is stronger than that predicted by renormalization group theory. For interactions between 70000 MW benzil-end-labeled polystyrene and varying MWs of anthracene-end-labeled polystyrene at 300 g/L polymer, k_q decreases by a factor of 10 in going from MWs of 100 to 1000 g/mol; beyond 1000 g/mol, k_q is nearly independent of chain length. Such effects indicate that the importance of oligomeric radical self-diffusion and polymer radical chain-end segmental mobility must be carefully considered in understanding the termination process in free radical polymerization. © 1996 John Wiley & Sons, Inc.     

Dynamics of end-grafted polystyrene brushes in theta solvents

The dynamics of the concentration fluctuations in end-grafted polystyrene brushes in a theta solvent (cyclohexane) are probed by evanescent wave dynamic light scattering at different wavevectors q and temperatures. When the solvent quality changes from marginal to poor, the relaxation function C(q, t) exhibits strong effects as compared with the smooth variation of the brush density profile. From a single exponential above 50 °C, C(q, t) becomes a two-step decay function. The fast decay is still assigned to the cooperative diffusion albeit slower than in the good solvent regime whereas the slow nonexponential and nondiffusive process might relate to microsegragated and/or chain dynamics in the present polydisperse brush. The relaxation function of the present three brushes with different grafting density reveals similarities and disparities between wet brushes and semidilute polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3590–3597, 2006     

Modeling and Experimentation of RAFT Solution Copolymerization of Styrene and Butyl Acrylate,Effect of Chain Transfer Reactions on Polymer Molecular Weight Distribution

Chain transfer reactions widely exist in the free radical polymerization and controlled radical polymerization, which can significantly influence polymer molecular weight and molecular weight distribution. In this work, the chain transfer reactions in modeling the reversible addition–fragmentation transfer (RAFT) solution copolymerization are included and the effects of chain transfer rate constant, monomer concentration, and comonomer ratio on the polymerization kinetics and polymer molecular weight development are investigated. The model is verified with the experimental RAFT solution copolymerization of styrene and butyl acrylate, with good agreements achieved. This work has demonstrated that the chain transfer reactions to monomer and solvent can have significant impacts on the number‐average molecular weight (M_n) and dispersity (Ð).     

Dependence of Polymer Chain Entanglements on the Solution Concentration

For the viscometric determination of molecular weights of polymers, sufficiently dilute solutions have to be used so that entanglements of the polymer chain are absent. The concentration of the polymer should be such that the relative viscosity (η_r) lies in the range 1.1–1.5 [1]. Similarly, for molecular weight determination by light scattering, the suggested concentration for polymer with weight-average molecular weight ( M _w ) > 10⁵ is 0.5 wt%; for those with M _w < 10⁵, up to 1% may be used [2].

The limits of polymer concentration for such measurements are not clearly known. On dissolution, the polymer molecules adopt a more or less extended configuration whose shape depends on the structure and molecular weight of the polymer, the properties of the solvent, and the temperature

[3]. The molecules of flexible linear polymers acquire a coiled configuration due to free rotation about the C-C bonds. When a dilute solution satisfies theta conditions, the polymer molecules are free from all kinds of interaction and move freely. Then their solution properties could possibly be related to their end-to-end distance. Based on this concept, our attempt to establish the permissible limits of polymer concentration for dilute solutions of several polymers of different molecular weights is reported here.     

On microphase segregation of interpenetrating polymer networks

The topological entanglements between subchains of two interpenetrating polymer networks are described in the simplest approximation supposing that the primitive path of each subchain is influenced due to the shift of one network relatively to the other. The entanglement contribution to the free energy of the networks is shown to behave as 1/q² for the state with deviation from uniform densities with the wave vector of order q. This contribution is shown to cause the microphase type of segregation.     

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.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.     

Reversible thermoresponsive behavior of poly(2-chloroethyl vinyl ether-<Emphasis Type="Italic">alt</Emphasis>-maleic anhydride) in mixed solvent of tetrahydrofuran/hexane

Poly(2-chloroethyl vinyl ether-alt-maleic anhydride) can exhibit lower critical solution temperature-type phase behavior reversibly by tuning the solvent composition in mixed solvent of tetrahydrofuran (THF) and hexane. The effect of solvent composition and polymer concentration on cloud point of polymer solution was investigated. The cloud point temperature for high molecular weight polymer was lower than that for lower molecular weight polymer. High resolution ¹H NMR spectra in mixed solvent of THF-d ₈ and hexane were also measured for comprehending thermoresponsive behavior of polymer solution in molecular level; however, any discontinuous change in the NMR signals around the cloud point could not be recognized.     

Scaling and structural properties of a polymer in a simple solvent: A study based on integral equations

We present a statistical mechanical theory for polymer–solvent systems based on integral equations derived from the polymer Kirkwood hierarchy. Integral equations for pair monomer–monomer, monomer–solvent, and solvent–solvent correlation functions yield polymer–solvent distribution, chain conformation in three dimensions, and scaling properties associated with polymer swell and collapse in athermal, good, and poor solvents. Variation of polymer properties with solvent density and solvent quality is evaluated for chains having up to 100 bonds. In good solvents, the scaling exponent v has a constant value of about 0.61 at different solvent densities computed. For the athermal solvent case, the gyration radius and scaling exponent decrease with solvent density. In a poor solvent, the chain size scales as N^v with the value of the exponent being about 0.3, compared with the mean field value of ⅓. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3025–3033, 1998     

Polymer deformation in various flows

Using a Langevin-like approach, the deformation of a polymer, modelled as a bead-spring chain, is calculated in simple shear, elongational and Kramers potential flow. Analytic expressions for the mean-square end-to-end distance, radius of gyration, segment-segment distance, static structure factor up to O(q⁴) and the intrinsic elongational viscosity are given. Near equilibrium, preaveraged hydrodynamic interaction is taken into account.     

Interaction of blockcopolymer micelles as probed by small-angle neutron and by small-angle X-ray scattering

 The analysis of the interaction of micelles formed by a blockcopolymer is given by means of small-angle X-ray (SAXS) and small-angle neutron scattering (SANS). The blockcopolymer consists of poly(styrene) and poly(ethylene oxide) (molecular weight of each block: 1000 g/mol) and forms well-defined micelles (weight-association number: 400, weight-average diameter: 15.4 nm) in water. The internal structure has been studied previously (Macromolecules 29:4006 (1996)) by SAXS. There it has been shown that the micelles are spherical objects. The structure factor S(q) as a function of the scattering vector q (q=(4π/λ) sin (θ/2); λ: wavelength of the radiation in the medium; θ: scattering angle) can be extracted from both sets of small-angle scattering data (SANS: q≤0.4 nm^-1; SAXS: q≤0.6 nm^-1). It is shown that particle interaction in the present system can be described by assuming soft interaction which is modeled by a square-step potential. Received: 12 May 1997 Accepted: 9 July 1997     

Distribution functions and dynamical properties of stiff macromolecules

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q^8/3tp^1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Polymerization and copolymerization of trioxane: Factors influencing molecular weight and end groups

In bulk polymerization and copolymerization of trioxane with ethylene oxide, it has been shown that p-chlorophenyldiazonium hexafluorophosphate is a superior catalyst as compared to boron trifluoride dibutyl etherate (BF₃ · Bu₂O). Polymers and copolymers of significantly higher molecular weight have been obtained. The higher molecular weight has been attributed primarily to less inherent chain transfer during propagation, which in turn can be attributed to the superior gegenion PF₆^?. The polymerization proceeds via a clear period followed by sudden solidification. Faster polymerization and higher molecular weight polymers have been observed for homopolymerization than for copolymerization. The polymer yield obtained after solidification is determined by both rate of polymerization and rate of crystallization of polymers. These rates, in turn, are dependent on the catalyst concentration. The molecular weight is determined both by polymer yield and extent of inherent chain transfer. In the range of monomer to catalyst mole ration [M]/[C] = (0.5–20) × 10⁴ investigated, it has been found that in the higher range, the polymer yield is independent of the catalyst concentration and the extent of inherent chain transfer is inversely proportional to the half power of catalyst concentration: [M]/[C] = (0.5–8) × 10⁴ for homopolymerization and (0.5–3) × 10⁴ for copolymerization with 4.2 mole % ethylene oxide. In the lower range, the yield decreases with catalyst concentration and the extent of inherent chain transfer is inversely proportional to higher power of catalyst concentration. The dependence of molecular weight of polymers on catalyst concentration has been shown to be a complex one. The molecular weight goes through a maximum as the catalyst concentration is decreased. The maximum molecular weights have been obtained at [M]/[C] ≈ 8 × 10⁴ for homopolymerization and ～3 × 10⁴ for copolymerization with 4.2 mole % ethylene oxide. Prior to reaching maximum the molecular weight is inversely proportional to the half power of catalyst concentration indicating it is primarily controlled by inherent chain transfer. Upon further decrease of catalyst, molecular weight decreases as a result of both a decrease in polymer yield and an increase in inherent chain transfer. In copolymerization of trioxane and ethylene oxide, it has been ascertained that methylene chloride exhibits a favorable solvating effect. Although higher inherent chain transfer takes place in copolymerization than in homopolymerization, the extent of chain transfer is independent of ethylene oxide concentration. The difference in polymer yield and molecular weight a t different ethylene oxide concentrations is attributed primarily to the difference in k_p/k_t ratio. It also has been demonstrated that end capping of polymer chains can be accomplished by the use of a chain transfer agent—methylal.     

Rheological Behavior and Scattering Studies of Acrylamide-Based Copolymer Solutions

Summary: In this paper the chemical structure of an acrylamide-N,N-dihexylacrylamide copolymer was established by IR and NMR. Static and dynamic light scattering in formamide were used in order to evaluate the polymer structural parameters, such as weight-average molecular weight (M_w), second virial coefficient (A₂), radius of gyration (R_G), the form factor P(q) and the hydrodynamic radius (R_H). Additionally to the classical characterization, those results indicated the presence of aggregation, showing that formamide is not a very good solvent, as stated in earlier investigations. The rheological behavior in aqueous solutions was evaluated as a function of the salt concentration. The solutions presented an important viscosity increase in the presence of NaCl and did not show any sensitivity to the presence of CaCl₂. This result is in favor of the oil recovery especially in high salinity reservoirs.     

Role of chain transfer in heterogeneous polymerization of ethylene

The role of chain transfer was studied for the radiation-induced polymerization of ethylene in precipitating media, namely n-butyl alcohol, tert-butyl alcohol and their mixtures. The affinities of those solvents for polyethylene are similar, but the chain-transfer coefficient of n-butyl alcohol is larger than that of tert-butyl alcohol. The polymerizations were carried out in a reactor of 100 ml under a pressure of 300 kg/cm², at 60°C, dose rate of 3.07 × 10⁴–1.75 × 10⁵ rad/hr in the presence of 50 ml of solvents. The polymerization in tert-butyl alcohol shows the kinetic behavior characteristic of a heterogeneous polymerization, such as rate acceleration, high dose rate dependence of polymerization rate, and low dose rate dependence of polymer molecular weight, whereas the polymerization in n-butyl alcohol does not exhibit such behavior and gives polymer having a molecular weight much lower than that of polymer obtained in tert-butyl alcohol. The polymer formed in tert-butyl alcohol exhibits a bimodal molecular weight distribution measured by gel permeation chromatography. In mixed tert-butyl alcohol and n-butyl alcohol solvent, with increasing fraction of n-butyl alcohol, the two peaks not only shift to lower molecular weight but the higher molecular weight peak becomes relatively small. Eventually, the polymer formed in n-butyl alcohol exhibits a unimodal distribution. Those results are well explained on the basis of the proposed scheme for heterogeneous polymerization.     

Dynamic Monte Carlo Simulation on the Polymer Chain with One End Grafted on a Flat Surface

A linear polymer chain in good solvent condition with one end grafted on a infinitely large, impenetrable flat surface is investigated using dynamic Monte Carlo simulation on a simple cubic lattice. Chain shape and dimension, angular correlation between the direction of the end‐to‐end vector and that of the longest principal axis of inertia are studied and discussed. Results reveal that the asphericity of end‐grafted polymer chains is greater than that of free ones, the limit ratio 〈L₁²〉 : 〈L₂²〉 : 〈L₃²〉 is about 1 : 3.0 : 14.9. The limit of mean angle 〈θ〉 of end‐grafted chains is about 22°, smaller than that of free chains, indicating angular correlation between the direction of the end‐to‐end vector and that of the longest principal axis is reinforced.