Physical properties, crystallization kinetics, and spherulitic growth of well-defined poly(ε-caprolactone)s with different arms

Both well defined star-shaped poly(ε-caprolactone) having four arms (4sPCL) and six arms (6sPCL) and linear PCL having one arm (LPCL) and two arms (2LPCL) were synthesized and then used for the investigation of physical properties, isothermal and nonisothermal crystallization kinetics, and spherulitic growth. The maximal melting point, the cold crystallization temperature, and the degree of crystallinity of these PCL polymers decrease with the increasing number of polymer arms, and they have similar crystalline structure. The isothermal crystallization rate constant (K) of these PCL polymers is in the order of K_2LPCL>K_LPCL>K_4sPCL>K_6sPCL. Notably, the K of linear PCL decreases with the increasing molecular weight of polymer while that of star-shaped PCL inversely increases. The variation trend of K over the number of polymer arms or the molecular weight of polymer is consistent with the analyses of both nonisothermal crystallization kinetics and the spherulitic growth rate. These results indicate that both the number of polymer arms and the molecular weight of polymer mainly controlled the isothermal and nonisothermal crystallization rate constants, the spherulitic growth rate, and the spherulitic morphology of these PCL polymers.     

Dielectric relaxation and molecular dynamics in poly(vinyl pyrrolidone)-ethyl alcohol mixtures in pure liquid state and in non-polar solvent

Dielectric relaxation and molecular dynamics in poly(vinyl pyrrolidone)-ethyl alcohol (PVP-E) mixtures with varying concentration in pure state and also in very dilute solutions of benzene were studied for their molecular conformation at 35 °C. Dielectric permittivity ε′ and dielectric loss ε″ of PVP-E mixtures were measured by a time domain reflectometry technique in the frequency range 10 MHz to 10 GHz. The value of static dielectric constant ε₀, dielectric relaxation time τ, and dielectric free energy of activation ΔF_τ has been evaluated by fitting the complex dielectric data into Debye equation. The variation in ε₀ was discussed by considering the volume effect and the structuring effects of the PVP on ethyl alcohol molecules. The formation of cooperative domains between PVP and ethyl alcohol molecules, CD_PVP-E and between the ethyl alcohol-ethyl alcohol molecules CD_E and their dynamics in the PVP-E mixtures were explored by using the evaluated values of τ and ΔF_τ.The PVP-E mixtures of low PVP concentration were also studied in very dilute solutions of benzene at 10.1 GHz. The value of average relaxation time τ₀, distribution parameter α, and relaxation time corresponding to the motion of small multimer species of alcohol molecules τ₁ and group rotation τ₂ has been determined. It has been observed that in dilute solution of benzene the value of τ₀ and τ₁ increases with the increase in concentration of PVP in PVP-E mixture but the τ₂ value is found independent of the mixture constituent concentration. The entanglement of the CD_PVP-E and the increase in the length of CD_E in dilute solution of benzene due to dissociation of the complexes between carbonyl and hydroxyl groups has been explored. The value of τ₂ is assigned to the rotation of -OH group about C-O bond in the ethyl alcohol species in dynamic equilibrium with larger steric hindrance due to hydrogen bonding.     

Partitioning of polymer chains in solution with a square channel: lattice Monte Carlo simulations

Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of confinement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coefficient K_c with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coefficient K_s with a slit of the same d. The chain with its bulk radius of gyration greater than ∼d/2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The K_c increased with an increasing polymer concentration φ_E in the exterior solution equilibrated with the channel. In a weak confinement, K_c closely followed K_s² of the same φ_E and d. The chains contracted at higher concentrations as they did in the bulk solutions. In a strong confinement, K_c was smaller than K_s² at the same φ_E in the semidilute regime, and, at higher concentrations, sharply increased to the value close to K_s².     

Partitioning of polymers into pores with surface interactions at dilute solution limit

The partitioning of a single polymer chain into a slit in a good solvent with different surface interactions is examined through Monte Carlo simulations from subcritical regime to adsorptive regime. The chain conformation in the subcritical regime is not perturbed by the surface interactions significantly. In the adsorptive regime, the conformation of the chain is strongly perturbed by the surface interactions. The confinement free energy in the two regimes maybe written in a uniform formula, βΔμ_conf∼c₁N(a/D)^xε_w+c₂N(a/D)^1/ν with x∼2.0 or larger in the subcritical regime and ∼1.0 in the adsorptive regime, where ν is the Flory exponent, D is the slit width, N is the chain length, a is the monomer size, and ε_w is the surface interaction energy between the polymer beads and the slit. This formula is valid for a long chain in the narrow slit in the subcritical regime or when the adsorption layer h>D in the adsorptive regime. A critical behavior occurs when ε_w is at the critical adsorption point and x=1/ν, then Δμ_conf will have little dependence on N or D. Higher order terms that are neglected in the above equation, however, may be present that could lead to a weak dependence of K on N and D even in the critical adsorption point.     

Brownian dynamics simulations of bead-rod-chain in simple shear flow and elongational flow

We have simulated a dilute polymer solution under simple shear and elongational flows using the bead-rod-chain model, by incorporating intra-chain hydrodynamic interaction and excluded volume effects. Configurational properties and rheological quantities were calculated. For the simple shear flow, shear rate dependencies of chain's size, shape, and rotation were monitored. Shear-thinning was observed at all shear rates. In addition, the critical strain rate, ε_c, at which the polymer undergoes a coil-stretch transition under elongational flow, was investigated. The slope at the inflection point of the log(R_g²) vs log(ε) curve increased as the chain length increased, indicating a possible first order transition, in agreement with theories and experiments.     

Acid dissociation constants of anilinium and mono-nitro anilinium ions in formamide

The acid dissociation constant of anilinium ion and those of o-, m- and p-nitro anilinium ions have been determined accurately in formamide over the temperature range 10–50°C (283.15–323.15 K) from the measurement of the emf of the cells, Pt, H₂/B(m₁), BHCl(m₂)/AgClAg.The dissociation constants at 25°C (298.15 K) have been checked by determining the same with the help of the cells, Pt, Q-QH₂/B(m₁), BHCl(m₂/AgClAg.Thermodynamical changes ΔG⁰, ΔH⁰ and ΔS⁰ for the dissociation processes have been evaluated. The results show that the dissociation constants of these conjugate acids are in general lower (pK_a's higher) in formamide than their corresponding values in water.     

Thermodynamics of sorption in and free volume of poly(5,6-bis(trimethylsilyl)norbornene)

Thermodynamics of sorption of n-alkanes C₄-C₁₁ in poly(5,6-bis(trimethylsilyl)norbornene) was studied using the Inverse Gas Chromatography (IGC). Temperature dependences of the specific retention volume V_g and solubility coefficient S of various alkanes were obtained in the range 60-140 °C. For solubility coefficients, the following equation holds: where T_c is the critical temperature of solutes, T is the experimental temperature and S is expressed in cm³(STP)/cm³ atm. The partial molar enthalpies ΔH_m and entropies ΔS_m of mixing of different n-alkanes in this glassy polymer vary in much wider range than in rubbers and display positive correlations: for more exothermic mixing process the larger negative ΔS_m values are observed. It was shown that the ΔH_m in poly(5,6-bis(trimethylsilyl)norbornene) pass through a minimum, when the size of solutes increases. The coordinates of ΔH_m at minimum versus solute size provide an estimate of the size of free volume elements in this polymer. This conclusion was supported by variation of permeability in different glassy polymers studied using IGC and by the results of other methods for probing free volume in glassy polymers.     

Experimental determination of the thermodynamic parameters affecting the adsorption behaviour and dispersion effectiveness of PCE superplasticizers

For adsorption of three different allylether-based PCE superplasticizers on CaCO₃ surface, the thermodynamic parameters ΔH, ΔS and ΔG were determined experimentally. The GIBBS standard free energy of adsorption ΔG_0ads, the standard enthalpy of adsorption ΔH_0ads and the standard entropy of adsorption ΔS_0ads applying to an unoccupied CaCO₃ surface were obtained via a linear regression of ln K (equilibrium constant) versus 1 / T (VAN'T HOFF plot). Additionally, the thermodynamic parameters characteristic for a CaCO₃ surface loaded already with polymer (isosteric conditions) were determined using a modified CLAUSIUS-CLAPEYRON equation.For all PCE molecules, negative ΔG values were found, indicating that adsorption of these polymers is energetically favourable and a spontaneous process. Adsorption of PCEs possessing short side chains is mainly instigated by electrostatic attraction and a release of enthalpy. Contrary to this, adsorption of PCEs with long side chains occurs because of a huge gain in entropy. The gain in entropy results from the release of counter ions attached to the carboxylate groups of the polymer backbone and of water molecules and ions adsorbed on the CaCO₃ surface. With increased surface loading, however, ΔG_isosteric decreases and adsorption ceases when ΔG becomes 0. The presence of Ca²⁺ ions in the pore solution strongly impacts PCE adsorption, due to complexation of carboxylate groups and a reduced anionic charge amount of the molecule. In the presence of Ca²⁺, adsorption of allylether-based PCEs is almost exclusively driven by a gain in entropy. Consequently, PCEs should produce a strong entropic effect upon adsorption to be effective cement dispersants. Molecular architecture, anionic charge density and molecular weight as well as the type of anchor groups present in a superplasticizer determine whether enthalpy or entropy is the dominant force for superplasticizer adsorption.     

Interaction between polymers in dilute solutions of two polymers in a single solvent measured by light scattering and the compatibility of polymers

The intensity of light scattered from dilute solutions of mixtures of two nonidentical polymers in a single solvent was measured. The parameter A₂₄ characterising the thermo-dynamic interaction of two nonidentical polymer molecules in solution was calculated for several systems polymer 2 - polymer 4 - solvent. For chemically strongly different polymers, A₂₄ is independent of molecular weights of the polymers and probably also of solvent. A₂₄ is related to the compatibility of both polymers and decreases contrary to expectation with increasing chemical difference between polymers 2 and 4.     

Theoretical evaluation of the conformational entropy of fusion and the melting temperature of polymers

A method is presented to theoretically estimate the conformational entropy ΔS_c of fusion of polymer chains of any stereochemical constitution. The effect of the type of crystalline conformation and the conformational energy differences on ΔS_c is discussed with examples. The dependence of ΔS_c on the configurational partition function is traced. A method for theoretically evaluating the melting temperature of a polymer from its conformational characteristics is presented. The application of the method to a total of 11 polymers leads to good agreement between the calculated and experimental values of the melting temperatures.     

Phase separation in randomly charged polystyrene sulphonate ionomer solutions

The dynamics of randomly charged polystyrene caesium-sulfonate ionomers in semi-dilute solutions were studied using a combination of dynamic light scattering (DLS), small angle neutron scattering (SANS), and bulk rheology. The samples were studied in toluene solutions where the aggregation of the dipolar groups is favoured. Evidence of aggregation in dilute solution is found using DLS and SANS with both the hydrodynamic and static radius of gyration indicating that there is a contraction of the chains due to intra-chain attractive forces. SANS experiments demonstrate the evolution of the aggregates into a network structure as a function of polymer concentration. The association process is caused by the dipolar attraction between the charged groups and introduces two static correlation lengths in the mesh structure of the network; the standard semi-dilute mesh size (ξ=1.12c^{−0.72±0.03}) and an inhomogeneity length (Ξ=24c^0.58±0.05) due to micro-phase separation. The scaling of the amplitudes of the correlation lengths I₁(0)∼c^{−0.33±0.07} and I₂(0)∼c^2.0±0.4 are consistent with good solvent conditions and micro-phase separation, respectively. An imposed shear causes the break up of the micro-phase separated micellar system with a characteristic yield stress for the Bingham step-like shear thinning.     

Weighted intrinsic viscosity relationships for polysaccharide mixtures in dilute aqueous solutions

The weighted intrinsic viscosities of polysaccharide mixtures in dilute aqueous solutions have been studied. The purpose of this investigation is to demonstrate that average intrinsic viscosities would scale with the weight fraction of the individual components for polysaccharide mixtures in 0.5N NaOH_(aq). The polysaccharides examined in this study were composed of polymers differing in their molecular weights, degree of branching, and bond linkages. Excellent agreement between theory and experiment was observed for the three different mixed polymer systems examined. This observation validates certain aspects of proposed theoretical treatments which employ this fundamental assumption and allows for further advances in experimental analytical developments of water-soluble polymer systems.     

Thermodynamics of ionization of some fluorinated β-diketones

Thermodynamic ionization constants, TpK_a, of several fluorinated β-diketones, viz. 2-furoyltri-fluoroacetone, heptafluorobutrylpivaloyl methane, hexafluoroacetylacetone, 2-thenoyltrifluoroacetone and trifluoroacetylacetone have been determined pH-metrically in 0-70vol.% dioxane-water mixtures at 25 and 35±0.01°C applying an empirical pH correction for mixed hydro-organic media. The pK_as in aqueous medium (at 0% dioxane) are obtained following the method of extrapolation and least-squares. All of them are very weak monoprotic acids. TpK_as do not vary linearly with the reciprocal of dielectric constant of the medium, but a plot of TpK_avs the mole fraction of dioxane is linear at a given temperature. The “true constant” K′_a and solvation number, n, in the expression (H⁺)(A⁻)/(HA)=K′_a(S)ⁿ=K^*_a for these reagents have been evaluated by analysing the experimental data mathematically. Values of ΔG°, ΔH° and ΔS° are also computed. Positive values of ΔH° found in aqueous-dioxane media for the above fluorinated derivatives, except HFOD, indicate the endothermicity of the proton enolization reactions. Temperature, medium as well as substituent effects are briefly discussed.     

A simple viscoelastic model for fatigue crack propagation in polymers as a function of molecular weight

A simple theory is presented to explain the strong influence of molecular weight (M) on rates of fatigue crack propagation (FCP) in amorphous polymers. It is proposed that the equation describing FCP rates may be expressed as the product of two functions, one involving the stress intensity factor (ΔK), and the other characterizing the relaxation process occurring in the plastic zone. To provide a physical network in the plastic zone that can sustain fatigue loading, it is proposed that one needs a sufficient fraction of molecular fibrils per unit area ($\text{W1}$) whose lengths are greater than M_c, the critical value of M required for entanglement. This effect can be summarized as a generalized rate process (confined at the plastic zone) expressed by A exp (Bσ) where σ is a stress and A and B are constants (B including the volume of activation). It is deduced that M influences the activation volume through the values of $\text{W1}$ and W, the weight fraction of molecules whose M>M_c. Using the equation developed it was possible to correlate FCP data of PVC and PMMA as a function of M with a high degree of confidence. Also, the value of activation volumes obtained compared favourably with those in the literature for static tests. The complementary value of $\text{W1}$ for these polymers was also seen to approximate closely to the void fraction in a craze. Extension to other cases such as semi-crystalline materials also seems possible.     

Mechanistic studies of protein refolding facilitated by like-charged polymers

The mechanism of lysozyme refolding facilitated by like-charged polymers was studied using cationic polyelectrolytes of different molecular weights and structures. Lysozyme refolding yield increased with increasing the total charge ratio (R) of the charged polymer to lysozyme in the refolding solution till reaching a plateau at a critical total charge ratio (R_c). The same R_c was observed for different polymers. Similarly, there was a critical minimum polymer molecular weight (M_c) for the facilitated protein refolding, below which the refolding yield decreased. The refolding yield was independent of the charge group structures in polymer. Fluorescence spectroscopy revealed that the polymers had no effect on the protein folding kinetics. Two physical models were proposed to explain the mechanism of the facilitated refolding and the meanings of R_c and M_c. The facilitating effect was attributed to the electrostatic interaction-induced oriented alignment of multiple protein molecules near the polymer chains, which maximizes the electrostatic repulsion between neighboring protein molecules, leading to the inhibition of protein aggregation. The studies provided insight into the mechanism of like-charged polymer-facilitated protein refolding, which would help develop more efficient polymers/particles for facilitated protein refolding applications.     

Electrospinning of linear homopolymers of poly(methyl methacrylate): exploring relationships between fiber formation, viscosity, molecular weight and concentration in a good solvent

A series of seven linear homopolymers of poly(methylmethacrylate) ranging from 12,470 to 365,700 g/mol M_w, were utilized to further explore scaling relationships between viscosity and concentration in a good solvent at 25 °C and to investigate the impact of these relationships on fiber formation during electrospinning. For each of the polymers investigated, chain dimensions (hydrodynamic radius and radius of gyration) were measured by dynamic light scattering to determine the critical chain overlap concentration, c^*. The experimentally determined c^*, was found to be in good agreement with the theoretically determined value that was calculated by the criteria c^*∼1/[η], where the intrinsic viscosity was estimated from the Mark-Houwink parameters, K and a (at 25 °C in dimethyl formamide) obtained from the literature. The plot of the zero shear viscosity vs. c/c^* distinctly separated into different solution regimes, viz. dilute (c/c^*<1), semidilute unentangled (1<c/c^*<3) and semidilute entangled (c/c^*>3). The crossover between semidilute unentangled and semidilute entangled regimes in the present investigation occurred at c/c^*∼3, which, therefore, marked the onset of the critical chain entanglement concentration, c_e, according to the procedure utilized by Colby and co-workers [Colby RH, Rubinstein M, Daoud M. J de Phys II 1994;4(8):1299-310. [52]]. Electrospinning of all solutions was carried out at identical conditions to ascertain the effects of solution concentration, molecular weight, molecular weight distribution and viscosity on fiber formation and morphological features of the electrospun material. Only polymer droplets were observed to form from electrospinning of solutions in the dilute concentration regime due to insufficient chain overlap. As the concentration was increased, droplets and beaded fibers were observed in the semidilute unentangled regime; and beaded as well as uniform fibers were observed in the semidilute entangled regime. Uniform fiber formation was observed at c/c^*∼6 for all the narrow MWD polymers (M_w of 12,470-205,800 g/mol) but for the relatively broad MWD polymers (M_w of 34,070 and 95,800 g/mol), uniform fibers were not formed until higher concentrations, c/c^*∼10, were utilized. Dependence of fiber diameter on concentration and viscosity was also determined, viz. fiber dia∼(c/c^*)^3.1 and respectively. These scaling relationships were in general agreement with that observed by Mckee et al. [McKee MG, Wilkes GL, Colby RH, Long TE. Macromolecules 2004;37(5):1760-67. [33]].     

Alpha relaxation study in poly(vinyl chloride)/poly(ethyl methacrylate) blends using thermally stimulated currents

Thermoelectrets of poly(vinyl chloride) (PVC) and poly(ethyl methacrylate) (PEMA) blends were prepared using the conventional thermal poling method. α‐Relaxation in this polyblend was investigated using thermally stimulated depolarization currents (TSDC). The global spectra of the polyblends revealed that the two polymers are not completely compatible. An Eyring relationship was verified through the linear relation between the activation enthalpy ΔH and the activation entropy ΔS. In addition, the thermal sampling (TS) data were used to determine the compensation parameters such as compensation temperature T_c and compensation time (τ_c). These parameters were used to calculate the density of disorder (DOD) for all samples, which was found to be close to 32%. © 2000 Society of Chemical Industry     

Free energy and confinement force of macromolecules in a slit at full equilibrium with a bulk solution

Nondilute athermal and theta solutions of nonadsorbing flexible macromolecules in equilibrium with repulsive slit-like pores were examined by the lattice Monte Carlo simulations. The free energy of confinement ΔA/kT and the force f/kT exerted by polymers on the slit were computed as a function of the slit width D in a wide range of bulk concentrations φ. The free energy and force profiles in nondilute solutions were found to deviate considerably from the ideal chain theory; the perturbation of chains by a presence of the slit walls were substantially reduced in nondilute solutions. The free energy and force functions appropriate for nondilute solutions were derived by fitting the simulation data. Further, the relative pressure p_I/p_E exerted by the nonadsorbing confined molecules on the slit walls was calculated. The depletion effect relevant to colloid stabilization was found in dilute solutions to be slightly weaker for excluded-volume chains than for ideal chains. The relative pressure equation was modified to cover semidilute solutions, by using the mean-field and scaling expressions of the osmotic pressure. Both the relative pressure p_I/p_E and the intra-slit concentration profiles φ_I(x) in tandem display a suppression of the depletion effect with increasing φ in simidilute solutions.     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002