Mark-Houwink Coefficients Research Articles

Investigating the Influence of Phosphate Ions on Poly(l-lysine) Conformations by Taylor Dispersion Analysis

In this work, the influence of the ionic strength and phosphate ions on poly(l-lysine) hydrodynamic radius, conformation and persistence lengths has been studied for molar masses comprised between 3000 and 70 000 g/mol. Mark–Houwink coefficients have been obtained via the determination of poly(l-lysine) hydrodynamic radius using Taylor dispersion analysis. The influence of phosphate ions and ionic strength on the solvent quality (poor, Θ, or good solvent) for poly(l-lysine) have been studied in details. Quantitative data on hydrodynamic radius, persistence length, Mark–Houwink coefficients are provided at pH 7.4, in the range of 10 mM to 1 M ionic strength, and for different phosphate ion concentrations from 0.1 mM to 50 mM under physiological conditions (154 mM ionic strength, pH 7.4). The strong influence of phosphate ions on poly(l-lysine) properties was finally illustrated by studying the interactions (stoichiometry, binding constant, and cooperativity) between poly(l-lysine) of DP 50 and human serum albumin, in the absence and in the presence of phosphate ions at pH 7.4.

Size exclusion chromatography and viscometry in paper degradation studies. New Mark-Houwink coefficients for cellulose in cupri-ethylenediamine

The paper deals with the application of size exclusion chromatography (SEC) for the studies of paper degradation phenomena. The goal is to solve some of the technical problems connected with the calibration of multi-detector SEC system and to find the correlation between SEC and viscometric results of degree of polymerization of cellulose. The results gathered for the paper samples degraded by acidic air pollutant (NO 2) are used as an example of SEC–MALLS application. From the correlation between intrinsic viscosities and absolute value of molecular masses obtained with SEC/MALLS (Multi Angle Laser Light Scattering) technique, Mark-Houwink coefficients for cellulose in cupri-ethylenediamine solution were determined. Thus obtained coefficients were used for the determination of viscometric degree of polymerization (molecular mass) of the aged samples. An excellent correlation was found between the chromatographic values of molecular masses obtained with SEC–UV/VIS detection and the viscometric ones utilizing the improved values of Mark-Houwink coefficients.

Solution Properties of Poly(Methyl Methacrylate) in Dimethylsulfoxide

The solution properties of polymethylmethacrylate in dimethylsulfoxide were studied using multi-angle light scattering and an online viscometer coupled to size exclusion chromatography. The data demonstrate that DMSO is a suitable eluent for the determination of the molecular weight of PMMA by SEC. The Mark-Houwink coefficients K and α were determined as a function of temperature. At 35°C, DMSO is a theta solvent for PMMA, and it becomes a good solvent as the temperature increases. The unperturbed dimension Kθ was calculated using three different procedures. The data do not show evidence of a conformational transition controlled by the temperature such as the one reported in benzene and confirm the existence of a general relationship between the ratio K/Kθ and α. In the case of PMMA, the comparison of the dipole moment of the side group to that of the solvent can be used to predict the existence of a conformational transition.

On the number-average molecular weight of poly(1,4- trans isoprene) determined by conventional GPC

We became aware, in the course of our on-going research, that the number-average molecular weight of poly(1,4- trans isoprene) determined by conventional gel permeation chromatography (GPC) in tetrahydrofuran (THF) using polystyrene standards differs from its true value by a factor 2. As far as we know, the Mark-Houwink coefficients of this polymer in a widespread GPC eluent such as THF have never been determined. We provide in this contribution a simple relationship between the number-average molecular weight of poly(1,4- trans isoprene) determined by GPC in THF using polystyrene standards and its true value.

Size and shape of soil humic acids estimated by viscosity and molecular weight

Ultrafiltration fractions of three soil humic acids were characterized by viscometry and high performance size-exclusion chromatography (HPSEC) in order to estimate shapes and hydrodynamic sizes. Intrinsic viscosities under given solute/solvent/temperature conditions were obtained by extrapolating the concentration dependence of reduced viscosities to zero concentration. Molecular mass (weight average molecular weight ( M ¯ w ) and number average molecular weight ( M ¯ n )) and hydrodynamic radius ( R H ) were determined by HPSEC using pullulan as calibrant. Values of M ¯ w and M ¯ n ranged from 15 to 118 × 10 3 and from 9 to 50 × 10 3 (g mol −1), respectively. Polydispersity, as indicated by M ¯ w / M ¯ n , increased with increasing filter size from 1.5 to 2.4. The hydrodynamic radii ( R H ) ranged between 2.2 and 6.4 nm. For each humic acid, M ¯ w and [ η] were related. Mark–Houwink coefficients calculated on the basis of the M ¯ w − [ η ] relationships suggested restricted flexible chains for two of the humic acids and a branched structure for the third humic acid. Those structures probably behave as hydrated sphere colloids in a good solvent. Hydrodynamic radii of fractions calculated from [ η] using Einstein's equation, which is applicable to hydrated sphere colloids, ranged from 2.2 to 7.1 nm. These dimensions are fit to the size of nanospaces on and between clay minerals and micropores in soil particle aggregates. On the other hand, the good agreement of R H values obtained by applying Einstein's equation with those directly determined by HPSEC suggests that pullulan is a suitable calibrant for estimation of molecular mass and size of humic acids by HPSEC.

Intrinsic viscosity measurement of dilute emeraldine base solutions for estimating the weight average molecular weight of polyaniline

Aggregation of the emeraldine base (EB) form of polyaniline in dilute solution is a major problem, which prevents full understanding of the colligative and hydrodynamic properties of this polymer. However, when 2-methylaziridine (2MA) is added to a polar aprotic solvent, EB readily dissolves without aggregation. The reduced viscosities of dilute N-methyl-2-pyrrolidinone (NMP) solutions containing EB are linear functions of EB concentration in the presence of 2MA. The Mark-Houwink coefficients (α = 0.77, and K = 1.2 x 10 -4 ) for the EB/NMP/2MA system were determined by correlating their weight average molecular weight (M w ) values, determined by gel-permeation chromatography (GPC) relative to polystyrene standards, with their measured intrinsic viscosity values ([η]). The M w of any unknown EB sample may be reliably estimated by first measuring the sample's intrinsic viscosity, and then applying these a and K values with the Mark-Houwink equation.

Molecular weight distribution of commercial PVC

AbstractThe molecular weight distribution (MWD) of commercial suspension grade poly(vinyl chloride) (PVC) resins with K values from 50 to 93 and mass grade PVC resins with K values from 58 to 68 has been determined by size exclusion chromatography (SEC), using literature Mark‐Houwink coefficients. The MWD is characterized by the number average molecular weight (Mn), the weight average molecular weight (Mw) and the polydispersity (Mw/Mn). Our results for Mw are consistent with recently published data, but we find different results for Mn and consequently for Mw/Mn. The polydispersity of PVC increases with increasing K value. This effect can be explained by two mechanisms. The first mechanism is a reduced terminating reaction rate between two growing polymer chains (disproportionation) at higher molecular weight owing to the reduced mobility of the polymer chains. The second mechanism is long‐chain branching of molecules with high molecular weight which lets the molecules grow at two ends. For two examples graphs of the measured MWD are compared with the theoretically expected MWD.

Poly-?,?-(3-hydroxypropyl)-DL-aspartamide: A new drug carrier

Poly-α,β-(3-hydroxypropyl)-DL-aspartamide (PHPA) was synthesized by the ring-open reaction of polysuccinimide (PSI) and 3-hydroxypropylamine. The polymer was characterized by 1H-NMR, 13C-NMR, FTIR, and GPC. Mark–Houwink coefficients were obtained from viscometry and GPC measurements, K = 5.53 × 10−3 and α = 0.78 in water. The acute toxicity of PHPA was examined and it revealed no death in ICR mice up to the dose treated of 15.3 kg/kg, and hematological parameters showed no significant difference between treated and control animals. The potential use of PHPA as a drug carrier was also investigated. In a typical case, a contraceptive drug, norethindrone (NET), was bonded to PHPA, and the drug sustained released as long as 120 days an in vitro test. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2411–2417, 2000

Solution Properties of the Exopolysaccharide Produced by Pseudomonas Marginalis Strain HT041B1

The solution properties of the exopolysaccharide marginalan produced by Pseudomonas marginalis HT041B were investigated by means of low-angle laser light-scattering, capillary viscometry, and rheology. Potentiometric and viscosimetric data indicated the absence of a cooperative transition of the disorder-to-order type. The experimental findings obtained in dilute solution (Mark-Houwink coefficients, rigidity coefficient, characteristic ratio) suggested that the polymer behaves like a semiflexible chain which adopts a disordered conformation. The rheological behaviour of more concentrated marginalan solutions, as determined by means of both steady shear and oscillatory measurements, further confirmed the disordered conformational state of the polymer in solution. 1. Presented at the XVIIIth International Carbohydrate Symposium, Milan, Italy, July 21-26, 1996.

Molecular characterization of polysaccharides dissolved in Me 2NAc-LiCl by gel-permeation chromatography

Polysaccharides function in key roles in textiles, biomass, foodstuffs, and plant cell walls, in addition to pharmaceuticals and immunological interactions. Structural information is urgently needed, but the complexity of the polymers, their interactions, and poor solubility have been limiting aspects. The dilute solution behavior of polysaccharides representing typical classes of natural products was investigated via gel-permeation chromatography (GPC) using refractive index and viscometric detectors. The solvent of choice for high-molecular weight cellulose analysis, dimethylacetamide with lithium chloride (Me 2NAc-LiCl), was used for direct polysaccharide dissolution without extraction or derivatization. The utility of this aprotic solvent for effective characterization of carbohydrates was explored. The polysaccharides studied spanned a range of molecular sizes, branching configurations, and linkage types, i.e., celluloses, amyloses, amylopectins, dextrans, pullulans, and curdlan. In addition to molecular weight values and distributions, calculated parameters defining each polysaccharides' dilute solution characteristics (intrinsic viscosity, radius of gyration, Mark-Houwink coefficients) were determined. Comparison between polysaccharides of similar molecular weight differing either in their branching patterns or linkage distribution were made. The calculated values were correlated with theoretical results predicted in the available literature and/or with known results. Relations among polymer linkage type, molecular chain compositions, branching assessments, and solution properties are described.

Calculation of hydrolytic rate constants of poly(ortho ester)s from molecular weights determined by gel permeation chromatography.

To obtained rate constants from weight-averaged (Mw) or z-averaged (Mz) molecular weights for polymers of Schule-Flory distribution and undergoing random scission. These constants were compared with those obtained by parallel 1HNMR studies. The hydrolysis of two poly(ortho ester)s were followed by 1HNMR and gel permeation chromatography (GPC). Equations to convert number-averaged (Mn), Mw and Mz into fraction of backbone remaining (fc) were derived. First-order hydrolytic rate constants of two poly(ortho ester)s; DETOSU-HD and DETOSU-CDM were calculated using these relationships. The rate constants calculated from 1HNMR, Mz and Mw were 0.215, 0.21 and 0.182 hr-1, respectively, for DETOSU-CDM and 0.152, 0.086 and 0.038 hr-1 for DETOSU-HD. The large discrepancy in the rates determined by 1HNMR and GPC in the latter case was attributed to that the detector response (refractive index) of the monomers was lower than that of the high molecular weight polymer. The difference is small in the case of DETOSU-CDM, and the rates calculated from GPC data were comparable or nearly identical to that obtained from 1HNMR data. Although GPC can yield rapid and valuable kinetic data for the degradation of biodegradable polymers, the system, however, must be carefully calibrated to account for the variations in Mark-Houwink coefficients and in the response of the mass detector between the high and low MW polymers.

Dilute solution behavior and Mark‐Houwink constants for a non‐linear cationic polyelectrolyte

AbstractMark‐Houwink coefficients and radius of gyration dimensions are presented for six unfractionated cationic polyelectrolytes of the poly(dimethylamine‐epichlorohydrin‐ethylendiamine) type. The copolymer system was studied in .05M, .10M, and 1.0M NaCl, and .12M NaClO4 aqueous solutions. Their solution behavior, as studied by intrinsic viscosity and light‐scattering technique, suggests these polymers adopt a somewhat spherical or star‐like conformation in aqueous salt solutions.

Low‐angle laser light scattering–aqueous size exclusion chromatography of polysaccharides: Molecular weight distribution and polymer branching determination

AbstractA low‐angle laser light scattering detector (LALLS) used with size exclusion chromatography (SEC/LALLS) has been applied for the determination of molecular weight, molecular weight distribution (MWD), and degree of branching of polysaccharides in 0.5N NaOH aqueous solution. Data from both detectors [differential refractive index (DRI) and LALLS] are used to calculate the absolute molecular weight at each point in a sample chromatogram. The correct average molecular weight and MWD can be obtained without calibration methods used in conventional SEC. As a consequence of this technique, Mark—Houwink coefficients can be predicted from a single broad‐distribution, homopolymer without recourse to time‐consuming fractionation methods. Moreover, the hydrodynamic volume separation mechanism of SEC can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper, SEC/LALLS has been employed to obtain data about the branching parameters gv and gM for samples of amylose, amylopectin, starch, and glycogen. For three homopolymers (amylose, amylopectin, and glycogen), branching frequency (as measured by chemical means), and the branching parameters (gv and gM) are inversely related. This trend is consistent with theoretical predictions. For starch, a nonhomogeneous branching distribution is observed as a function of molecular weight.

Mark–Houwink–Sakurada constants and dilute solution behavior of heterodisperse poly(acrylamide-co-sodium acrylate) in 0.5M and 1M NaCl

Mark Houwink coefficients and molecular size parameters are presented for 31 unfractionated samples of polyacrylamide and hydrolyzed polyacrylamide in 0.5M and 1M aqueous NaCl. Polymers investigated include polyacrylamide, plus 10, 20, 50, 70, and 100 mol % poly(sodium acrylate). Their solution characteristics were studied by gel permeation chromatography, intrinsic viscosity, and light scattering techniques. A density function and heterodispersity index was assigned to each polymer sample due to the polydispersity of the molecular weight distributions. This technique improves the intrinsic viscosity–molecular weight correlation for heterodisperse commercially synthesized polymer systems. The intrinsic viscosity of these commercial compounds will yield useful estimates of their molecular weight, in spite of their obvious heterogeneity.

Synthesis and photochemical properties of poly(1-(4-carboethoxyphenyl)-2-propen-1-one)

New light-sensitive polymer, poly(1-(4-carboethoxyphenyl)-2-propen-1-one), M w = 1·3 × 10 6 Dalton, M w M n = 2·6 , was prepared. On the basis of fractions prepared by photolysis, Mark-Houwink coefficients ( α=0·79 ± 0·02 and K=(2·41 ± 1·4) × 10 −3) were determined in chlorobenzene at 25°C employing low-angle laser light scattering and automatic viscometry. Quantum yield of main chain scissions (The Norrish Type II Reaction) was 0·45 in benzene solution under 366 nm radiation at room temperature. The Stern-Volmer constant for quenching of photolysis by naphthalene in benzene was 171 mol −1 and 63 mol −1 by 2,5-dimethyl-2,4-hexadiene in chloroform. The OO band of phosphorescence (438 nm) of the polyketone prepared was bathochromically shifted in comparison with poly(1-phenyl-2-propen-1-one), λ max• = 409 nm. The transient spectrum measured by laser flash photolysis exhibited a maximum at 350 nm with a lifetime of 150 ns. The bimolecular quenching rate constant (k q) for 2,5-dimethyl-2,4-hexadiene in chloroform was 5·57 × 10 8 dm 3 mol −1 s −1. This value agrees well with k q = 4·2 × 10 8 dm 3 mol −1 s −1. based on the Stern-Volmer constant of photolysis quenching and lifetime estimated by laser flash photolysis.

Trifluoroethanol/chloroalkane mixtures: Excellent novel solvents for aliphatic polyamides

AbstractCertain mixtures of TFE/CHCl3 were found to be excellent solvents for aliphatic polyamides such as nylon‐6, nylon‐66, nylon‐11, nylon‐12, nylon‐69, nylon‐610, and nylon‐612. Intrinsic viscosities were measured and Mark–Houwink coefficients determined for nylon‐6/TFE/CHCl3, indicating TFE‐rich mixtures to be better solvents than TFE alone. Similar results were obtained for TFE/CH2Cl2. Four ternary phase diagrams were constructed for nylon‐6/TFE/chloroalkanes, of which the ones with CHCl3 and CH2Cl2 are the most interesting. In the nylon‐6/TFE/CHCl3 diagram higher nylon‐6 solubility in TFE‐rich mixtures and a biphasic region in the CHCl3‐rich compositions are evident. In the TFE/CH2Cl2 system, the higher dissolution of nylon‐6 is observed, but no biphasic regions are detected. In certain solvent compositions and/or polymer concentrations the polymer is incompletely soluble, making the phase diagrams rather complicated. Observed thermodynamic excess properties appear to relate to the quality of TFE/chloroalkanes as solvents for nylon‐6. Studies on swelling of nylon‐6 networks immersed in TFE/CHCl3 show a behaviour previously described by Krigbaum and Carpenter for a general case where the formation of contracts between molecules of the two solvents is discouraged and their preferential solvation of the polymer is, therefore, encouraged. The phenomena observed in this work can be qualitatively explained as arising from antagonistic interaction of TFE molecules with chloroalkane ones. The presence of the polyamides in solution reduces such contacts, enchancing the dissolution of the polymer in the (TFE‐rich) solvent mixtures.

Viscosity–molecular weight relationships for poly(ethylene terephthalate) in hexafluoroisopropanol–pentafluorophenol using SEC–LALLS

AbstractViscosity–molecular weight characterization of poly(ethylene terephthalate) (PET) in hexafluoroisopropanol (HFIP), pentafluorophenol (PFP), and HFIP/PFP is reported for the first time using size exclusion chromatography‐low angle laser light scattering (SEC–LALLS) measurements. These strong solvents are capable of dissolving PET under very mild conditions and therefore minimize polymer degradation. In addition these solvents are capable of dissolving PET samples which have poor solubility in more traditional PET solvents such as orthochlorophenol (OCP) and phenol/tetrachloroethane (PTCE). By combining molecular weight information, obtained without the need of any SEC calibration curves, with intrinsic viscosity measurements, on several broad molecular weight PET samples, the Mark–Houwink coefficients for the five PET–solvent systems mentioned above have been determined. The coefficients correspond to those which would be obtained by using a large number of relatively monodisperse samples of PET covering a molecular weight range of about 2 × 103 to 2 × 105. Data is also provided which shows that intrinsic viscosities for PET in HFIP, PFP, HFIP/PFP, OCP, and PTCE can be determined from a single viscosity measurement at a finite concentration. Data for interconverting intrinsic viscosities determined in any of these five solvents is also given.

Characterization of Copolymers and Polymer Mixtures by Gel Permeation Chromatography

Abstract Estimation of molecular weights from GPC data is complicated when the polymer sample consists of a mixture of homopolymers or of statistical copolymers with nonuniform compositions. This is because sizes of solvated polymer coils depend on solvent interaction with both the homo-and hetero-units of the copolymers and because the extent of solvation of different homopolymers can differ. The overall degree of solvation may change effectively with composition and use of a single “average” set of Mark-Houwink constants in calibration procedures will then produce false molecular weight data from the GPC data. A new molecular weight average, M x, is defined to overcome this problem. This average can be determined from the GPC chromatogram and intrinsic viscosity of the sample in the GPC solvent. Mark-Houwink coefficients are not needed. M x lies between M w and M z.

Calibration in High Temperature Gel Permeation Chromatography of Linear Polyethylenes

Abstract The mathematical relationship between the gel permeation chromatography calibration curves of polystyrene and linear polyethylene has been determined in 1,2,4-trichlorobenzene at 130, 135 and 140°C. The experimentally determined relationship is in good agreement with that predicted from application of the principles of the universal calibration technique and published Mark-Houwink coefficients. Definition of this relationship enables the use of polystyrene as a secondary standard for gel permeation chromatographic determination of linear polyethylene molecular weight determinations.

Prediction of osmotic pressures of polymer solutions

AbstractA theory which has been developed to account for the effects of concentration on the equivalent hydrodynamic volumes of dissolved polymers has been combined with a statistical mechanical relation for the virial coefficients of dilute suspensions of rigid spheres. With a scaling factor for solvent goodness, osmotic pressures of polymer solutions can be predicted with good accuracy. The input parameters needed are the number‐average molecular weight of the polymer sample and its intrinsic viscosity in the solvent of interest, as well as its intrinsic viscosity under theta conditions. The intrinsic viscosities can be estimated with sufficient accuracy from tabulated Mark–Houwink coefficients. The model developed contains no adjustable parameters. Comparisons of predicted and reported experimental osmotic pressures are presented, and a method for prediction of second virial coefficients is described.