Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Flow properties of branched polydisperse polymers

Viscosity and normal-stress difference as functions of shear rate were examined for poly(vinyl acetate) samples with various degrees of random branching in diethyl phthalate solution. At moderate concentration (c = 0.17 g/ml) the viscosities were depressed by branching, in fair accord with the Bueche theory. However, at higher concentrations (c = 0.35 g/ml) the data showed a progressive trend in the direction of viscosity enhancement by branching, a characteristic which has been observed by other workers in undiluted branched polymers. Accompanying viscosity enhancement was an increase in the temperature coefficient of viscosity, an increase in recoverable compliance (estimated from steady-state normal-stress data) and an early onset in the shear rate dependence of viscosity.     

Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

On rheological properties of polydisperse polymers

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: $\text{η}{}_0\text{～}\text{M}{}^{\mathrm{\alpha }}{}_{\mathrm{<mtext>w</mtext>}}$; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: , and in the general case α₁ ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.     

Viscosity and normal stresses in branched polydisperse polymers

The steady-flow behavior of five samples of branched poly(vinyl acetate) has been studied with the Weissenberg rheogoniometer. The branching densities and molecular weight distributions were known from an analysis of the polymerization kinetics. Measurements were made on concentrated diethyl phthalate solutions (0.170 and 0.225 g/ml) at temperatures of 30 and 70°C. The viscosities of all solutions at zero shear rate were less than of solutions of linear poly(vinyl acetate) with the same weight-average molecular weight. The amount of decrease was in excellent agreement with Bueche's theory of melt viscosity in branched systems. The viscosity versus shear rate curves were surprisingly independent of molecular weight distribution, the data from all samples being superimposable on the same master curve. Relaxation times derived independently from the viscosity behavior and the normal stress data were of similar magnitude and always close to the Rouse relaxation time of each solution.     

Analytical theory of ideal polydisperse polymers at interfaces

We use a recently developed continuum theory to present an exact treatment of the interfacial properties of ideal polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. We apply our theory to a number of cases, including, non-adsorbing and adsorbing surfaces, as well as telechelic chains.     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Predicting the behaviour of polydisperse polymers in liquid chromatography under isocratic and gradient conditions

In this paper we describe how the existing theories to describe retention and peak width in isocratic and gradient-elution liquid chromatography can be expanded to describe the retention behaviour of natural and synthetic repetitive polymers, which feature distributions of molecules with different masses (and often different structures) rather than unambiguous molecular formulas. For polydisperse samples, it is vital that the model accommodates (isocratic) elution of sample components before the onset of a gradient, elution during the gradient, and elution after the completion of the gradient. The expanded models can readily be implemented in standard spreadsheet software, such as Excel. We have created such spreadsheets based on the conventional model for retention in reversed-phase liquid chromatography (RPLC) and on two different models for retention in normal-phase liquid chromatography. The implementation allows an easy visualization of the theoretical concept. Up to three different polymeric series can be entered, with a total of up to 100 peaks being computed and displayed in isocratic or gradient-elution chromatograms. Also visualized are "retention models" (diagrams of isocratic retention vs. composition) and "calibration curves" (retention or elution composition vs. molecular mass or degree of polymerization). The coefficients in the isocratic retention model may be correlated, as has often been observed in RPLC. It is shown that under certain conditions such a correlation corresponds to the existence of so-called critical (isocratic) conditions, at which all the members of a given polymeric series (same composition and end groups, different number of repeat units) show co-elution.     

Competitive adsorption of a polydisperse polymer during emulsification: experiments and modeling

In this paper we study the selective adsorption of a high molar mass polymer, OSA-starch, at the cyclohexane/water interface during emulsification. This was made possible through the use of AsFlFFF-MALS-RI which enables us to characterize the size and molar mass of polydisperse ultrahigh molar mass polymers. The results show that the high molar mass components in the molar mass distribution of the polymer were selectively adsorbed. The selective adsorption is most likely due to convective mass transport in the turbulent flow fields, during formation of the emulsion, which favors transport to the interface of the high molar mass polymers in the sample. The rapid adsorption that occurs during emulsification is likely to give rise to nonequilibrium effects and jamming at the interface. Furthermore, we describe the adsorption process and illustrate its selective nature through a turbulent flow collision model.     

General description of the structure of branched polymers

A multidimensional distribution function is defined to describe the branching structure of branched homopolymers such as starch and polyacrylates. Averages of this function give distributions which can be measured using, for example, the number and weight distributions as a function of hydrodynamic volume from size‐exclusion chromatography and field‐flow fractionation, and two‐dimensional separation methods. This provides means to plot data to obtain physically meaningful quantities, and to test mechanistic postulates for the (bio)synthesis, of branched polymers. A simple enzyme‐kinetic model for a reduced form of this multidimensional distribution for starch biosynthesis is derived and solved. One application is to derive number distributions for the molecular weight distribution of debranched glycogen. Fitting this to experiment gives estimates of this ratio for two forms of glycogen. We propose that number distributions from size separation for starch (which, it is pointed out, are obtained directly from in‐line viscometric detection) have a simple and meaningful form when plotted as ln(number distribution) against V_h^p, where V_h is hydrodynamic volume, and p a parameter of order unity determined from multiple‐detection size separation measurements. The new function is also used to propose a two‐dimensional experiment which can yield an unambiguous measurement of the amylose: amylopectin ratio in starch. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3914–3930, 2009     

Relaxation by reptation and tube enlargement: A model for polydisperse polymers

Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self-consistency scheme. Thus, quantitative agreement remains incomplete.     

Methods of description of orientation in polymers

The nonrandom orientational distribution of structural units, such as crystallites and chain segments, prevailing in an anisotropic bulk polymer sample can be represented fully by an orientation distribution function. Measurements of fluorescence polarization and wide-line NMR are, in principle, capable of yielding information on the moments of the distribution function up to the fourth order. This work presents the method of analysis required to determine these moments. For this purpose, the distribution function is expanded in a series of generalized spherical harmonies. The method is an extension of a similar technique previously proposed for analysis of x-ray diffraction data for determination of a complete crystallite orientation distribution function.     

Modification of polymers by adsorption phenomena

The adsorption of ions and amphiphilic molecules on solid polymers is investigated by direct force measurements using an atomic force microscope (AFM). It is shown that electrolyte ions are changing the surface potentials of the solid polymers as well as their adhesive properties. The experiments show that the interaction with a negatively charged probe is dramatically decreased by the adsorption of anions. The adsorption isotherms are determined by zeta potential measurements (streaming potential of flat plates). In presence of adsorbing anions, the attractive interaction and the adhesion are reduced and can be eliminated completely. So, even solutions of simple electrolyte ions can be applied intentionally in order to modify the interaction of polymer surfaces. A wide variety of technological applications becomes accessible.     

Universal function for the description of multi-layer adsorption isotherms

In describing multi-layer adsorption it is common to use standard isotherms. To establish such isotherms experimental data are required at a wide range of adsorptive pressure. This paper presents the theoretical and experimental analysis of the new t _δ-method, which is suitable to predict type II multi-layer adsorption isotherms on the basis of only two adsorption values, measured in the area of mono- and multi-layer saturation and of the surface fractal dimension of the adsorbent.     

Hydrogen adsorption in microporous hypercrosslinked polymers

A microporous hypercrosslinked polymer resin was synthesized and shown to adsorb 3.04 wt.% hydrogen at 77 K and 15 bar; this represents the highest level of hydrogen adsorption yet observed for an organic polymer.     

铜离子印迹聚合物的吸附性能研究EI北大核心CSCD

以二苯氨基脲为功能单体,合成了铜离子印迹聚合物(Cu^(2+)-IIPs),并用于Cu^(2+)的快速吸附检测。对Cu^(2+)-IIPs进行了表征,考察了其对Cu^(2+)的吸附特性。结果表明,Cu^(2+)-IIPs为球型状颗粒且粒径分布均匀,印迹位点位于表面及空穴中,对Cu^(2+)的吸附过程符合准二级动力学模型,吸附速率受表面吸附和内部扩散共同影响。较之Langmuir模型和Tempkin模型,Freundlich模型能更好地拟合吸附等温线,说明属于多层吸附;ΔG^(0),ΔH^(0)和ΔS^(0)的数据显示,吸附是一个自发进行的、吸热的、熵增大的过程;Cu^(2+)-IIPs对Cu^(2+)的吸附量远大于具有相似结构和性质的其它重金属离子,因而具有良好的吸附选择性。     

New description of heterogeneity effects in adsorption from multicomponent solutions and liquid adsorption chromatography

General equations describing adsorption from solutions on solids and liquid adsorption chromatography with mixed mobile phases are formulated in terms of the bulk and surface activity coefficeints. Definition of the surface activity coefficients is extended; they describe nonideality of surface solution due to difference in molecular interactions of the components as well as nonideality of this solution generated by the adsorbent heterogeneity. It is shown that the above general equations predict simpler expressions known already in the literature.     

Water vapour adsorption on organic and inorganic polymers

Water vapour adsorption on polymers affects their processing behaviour and useful properties. Water vapour adsorption on organic polymers, silk, Nylon 6 fibres in undrawn and permanent set forms, polyester micro fibres, plasticised PVC films with 60 phr dioctylphthalate (DOP) and inorganic polymer sepiolite particles were investigated in this study. The materials were examined using the BET equation. The surface areas of silk, cast Nylon 6 and muss Nylon 6 were determined as 108, 46 and 23 m² g^–1, respectively. Sepiolite did not fit BET equation. Polyester and PVC adsorbed very small amounts of moisture.This revised version was published online in November 2005 with corrections to the Cover Date.     

Theoretical description of the adsorption and the wetting behavior of alkanes on water

The wetting behavior of alkanes of medium chain length (e.g., pentane, hexane, and heptane) on water is more complex than the usually observed first-order wetting transition from partial to complete wetting by showing a sequence of two transitions. In this sequential-wetting scenario, a first-order transition from a microscopically thin to a mesoscopically thick layer of liquid on the substrate surface is followed by a continuous divergence of the film thickness upon increase of the temperature. This critical transition to complete wetting at T(w,c) is solely determined by long-range interactions between substrate and adsorbate, which are well-described by Dzyaloshinskii-Lifshitz-Pitaevskii [Adv. Phys. 10, 165 (1961)] theory in terms of the static dielectric constants and the refractive indices of the media involved. The first-order thin-thick transition, however, which occurs at a lower temperature T(w,1), results from an interplay of short-range and long-range forces and is notoriously more difficult to describe because a satisfactory theory of the short-range interactions between substrate and adsorbate is still missing. The approach presented in this paper attempts to account for the short-range interactions in an effective way: Within a Cahn-type [J. Chem. Phys. 66, 3667 (1977)] theory that has been augmented for long-range interactions and modified to treat the first layer of adsorbed molecules in a lattice-gas approach, the contact energy is deduced from the surface pressure, which in turn is calculated using a two-dimensional van der Waals equation of state and an expression for the Henry's law constant that was derived by Hirasaki [J. Adhes. Sci. Technol. 7, 285 (1993)]. The method uses only the dielectric properties of the isolated bulk media and simple assumptions on the size and the shape of the adsorbed alkane molecules and leads to satisfactory results for the transition temperatures T(w,1) and T(w,c).