Quantitative Prediction of Concentration Effects in Steric Exclusion Chromatography

Abstract

A semiempirical model, based on a previous one quantitatively describing the dependence of the elution volume, V(c_A), on the concentration of injected polymer, c_A, in exclusion chromatography (SEC) at dilute solutions, has been developed. In the derived equation, concentration effects are mainly governed by the Huggins' coefficient, k_A, and by the quadratic coefficient in the polynomial expansion of the reduced specific viscosity, k_A. Because of the incertitudes on reliable k_A and k_A' values, these are respectively removed from the model through she Imai's equation and the empirical correlation k_A' + 0.122=k_A, here obtained. Thus, A predicted elution volumes besides polymer concentration only depend on the polymer intrinsic viscosity and on its unperturbed dimensions constant,K_θ. The polymer concentration range of model applicability is up to Jerately diluted polymer solutions, as a comparison between predicted and experimental elution volumes for diverse literature systems shows.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

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.     

Delayed fluorescence from the lowest 1B+3u state of anthracene,due to hetero-triplet—triplet annihilation of 3anthracene* and 3xanthone*

The P-type delayed fluorescence (DF) S_i→S_o of aromatic compounds results from the population of excited singlet states S_i by triplet—triplet annihillation (TTA) of molecules in their lowest and metastable triplet state T₁ : T₁ + T₁

S_i + S_o; S_i may be any excited singlet state whose excitation energy E(S_i ? 2 E(T₁). TTA of unlike molecules A and B (hetero-TTA) may lead to excited singlet states either of A or of B. In particular, if E(T_A¹) < E(T₁^B), hetero-TTA may lead to excited singlet states S_k^A which are not accessible by TTA of 2 T₁^A. In the present paper we report the first example of the detection of the DF from a very short-lived upper excited singlet state S_k^A which has been populated by hetero-TTA. The systems investigated are liquid solutions of A = anthracene-h₁₀ or anthracene-d₁₀ or 9,10-dimethylanthracene and B = xanthone in 1,1,2-trichlorotrifluoroethane at 243 K. S_k^A is the lowest ¹B_3U⁺ state (B_b state) of anthracene.     

Evaluation of Huggins' Constant,Kraemer's Constant and Viscosity Concentration Coefficient of Polymer Dextran in Urea,Glycine and Glucose

Abstract

Reduced viscosity (η_sp/c) and Inherent viscosity (In η_rel/c) of dilute solution of water soluble polysaccharide polymer “Dextran” has been calculated by measuring the flow time of the polymer solution in solvents like 6(M) Urea, 2(M) Glycine and 50% Glucosc at three different temperatures ? 25°C, 30°C and 35°C. From extrapolation of curve (η_sp/c) versus (c) and (In η_rel/c) versus (c), thermo viscosity parameters like Huggins' constant (k′_H) Kraemer's constant (k″_H) and viscosity concentration coefficient (a ₂) have been estimated which enable us to know the fate of the polymer molecules in these solvents.     

Self-diffusion and electron spin exchange of hydrophobic probes in dilute solution

Electron spin exchange rate constants have been measured by ESR spectroscopy for a nitroxide spin probe in a number of solvents, including water. The apparent collision rate constants (k _c ^′ ) calculated from the spin exchange rate constants showed marked deviations from the Smoluchowsky equation (k _c ^′ η=const), which were greatest in solvents of lowest viscosity. These effects are attributed to inefficiency of the spin exchange process. Self-diffusion coefficients (D) were measured for diamagnetic analogs of the nitroxide spin probe in similar solvent systems by pulsed field gradient NMR spectroscopy. TheD values gave reasonable agreement when corrected for viscosity (Dη=const). Collision rate constants calculated fromD were in good agreement with those measured by ESR in solvents of high viscosity. Thek _c ^′ value for the spin probe in water was significantly lower than that in isoviscous organic solvents. This effect is discussed in terms of a hydrophobic hydration shell for the spin probe which acts as an additional barrier to collision.     

Deformation of a Polymer Brush Immersed in a Binary Solvent

An analog of the Alexander‐De Gennes box model is used for the theoretical investigation of an external deformation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). The thermodynamics of a polymer in the solvents A and B is described by parameters χ_A and χ_B, χ_A > χ_B. The brush behavior under deformation is investigated with regard to solvent composition and polymer‐solvent interactions. It is shown that in a pre‐binodal range of the solvent composition Φ_B < Φ_B⁰ in the bulk (here Φ_B⁰ is a binodal value) there is such a value of Φ_B = Φ _B* that deformation does not affect solvent composition inside the brush. This invariant quantity Φ _B*, being a function of only thermodynamic parameters, is independent of the brush characteristics, such as grafting density. It is shown that two types of the first‐order phase transitions can arise in the system considered: a compositional phase transition induced by a change in the solvent composition in the bulk, and a deformational phase transition caused by an external deformation of the brush. The value of Φ _B* defines a borderline concentration of the admixture in the bulk; the brush behavior in the ranges 00 ⪇ Φ_B ⪇ Φ _B* and Φ _B* ⪇ Φ_B < Φ_B⁰ are different. If no compositional phase transition occurs in the system, the deformational phase transition should arise under stretching at Φ _B* ⪇ Φ_B. If the compositional phase transition exists, it is realized in the range Φ_B < Φ _B* and causes the deformational phase transition in this concentration range, not only under stretching, but also under compression. Microphase segregation inside the brush is demonstrated for both phase transitions despite overestimation of the brush homogeneity in the box model.     

The viscosities of dilute solutions of nitrocellulose

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

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Determination of Polymer Compatibility by Viscometric Measurements on Ternary Solutions of the Two Polymers

Results on the intrinsic viscosity [η] are reported for the system solvent(1)/polymer(2)/polymer(3) in which the solvent was benzene, polymer(2) was polystyrene (PS), and polymer(3) was poly(dimethylsiloxane) PDMS. The values of [η] were then used to determine the likely compatibility of polymer blends of PS and PDMS. Initial focus was on the traditional interaction parameter b ₂₃ ⁽¹⁾ used by several authors to predict compatibilities, it but depends on the molar mass, weight fractions, and concentrations of each polymer. A new interaction parameter b ₂₃ ⁽²⁾ that is independent of polymer(3) concentration and molar mass was evaluated for determinations of polymer compatibility.     

Pulsed NMR of cis-polyisoprene solutions T1 and T2 relaxations,free volume,viscosity relationships

Previous pulsed NMR studies of polyisoprene have largely been concerned with entangled or crosslinked networks. This paper deals with (i) the relaxation of high molecular weight entangled; (ii) cross-linked; (iii) monodisperse low molecular weight; and (iv) high molecular weight polymer in the presence of tetrachloroethylene which, by increasing molecular mobility, can be expected to influence the NMR relaxation. For all four types of polyisoprene, the spin-lattice T₁, relaxation shows a minimum with position depending only on the free volume, as influenced by changes in temperature T and polymer concentration v₁,. For monodisperse polyisoprene of molecular weight 7200, insufficient to form an entangled network, the spin-spin relaxation decay constant T_2L is quantitatively related to the free volume ₁ by two parameters A′ and B″ when the free volume is altered by a change in temperature, or in polymer concentration (10–100/). This can also be expressed in the form where the parameter T_∞ at 100% concentration agrees with the value used to describe rheological properties. At other concentrations of polymer, T_∞ and B′ can be derived quantitatively from the coefficients of volume expansion of polymer and solvent. The variation of T_2L with molecular weight (T_2L ∝ M^?0.5) occurs via the A′ parameter. It is concluded that T_2L can be quantitatively related to the free volume available for molecular motion (as influenced by temperature and solvent concentration) as well as to molecular weight. Furthermore T_2L is simply related to viscosity n, over a wide range of temperatures and concentrations. T₂ can be used to analyse the molecular motions involved in theology.     

A2Σ+ → X2Πi emission spectra of the phosphaethyne cations HCP+ and DCP+

Electron impact excited $\text{A}$²Σ⁺ → $\text{X}$²Π_i emission spectra of HCP⁺ and DCP⁺ have been observed. The spectra consist of short progressions in ν″₃. The 0 0⁰0 → 0 0¹0 bands have been studied under high resolution and rotational analyses carried out. Some of the more important derived constants are (in cm^?1) HCP⁺; ν^″₃ = 1150(10), A^″₀ = -146.97(3), B^″₀ = 0.6224(16), B^′₀ = 0.6690(17); DCP⁺; ν^″₃ = 1110(10), A^″₀ = -146.71(1), B^″₀ = 0.5284(2), B^′₀ = 0.5682(2).     

Exciton transitions in quasi-one-dimensional crystals. 9,10-dichloroanthracene

Polarized reflection spectra of the first singlet transition of the α-crystalline form of 9,10-dichloroanthracene are reported. Crystal faces (001), (011) and (010) were examined in spectral range 450 to 350 nm at two temperatures, 5 K and 300 K. Two systems of transitions were observed. The first system is assigned to neutral excitons. Spectral similarities with unsubstituted anthracene and arguments based on the one-dimensional stacking of molecules are used to construct a model of the exciten band structures. The M-polarized ππ* molecular transition gives rise to a four branch band with two allowed transitions. The 0-0_b (A_g → A_u) transition lies 50–100 cm^?1 above the bottom of the exciton band and the 0-0_c′ (A_g → B_u) transition lies at the top of the band. In the reflection spectrum the Davydov splitting c′b for transverse excitons is 210 cm^?1. The exciton band of the 00 molecular transition is not isolated but overlaps the two-particle manifold of the 0–1 vibronic transition. As a result of the 0–1_c′ transition is unexpectedly strong in the spectra of the (010) face. The second system is polarized along the stack-axis a and starts 2500 cm^?1 above the first system. It is tentatively assigned as |a(A_g → B_u) charge transfer exciton transition in agreement with earlier observations.     

Chromatographic Characterization of Molecularly Imprinted Microspheres Synthesized by Aqueous Microsuspension Polymerization：Influences of pH,Kinds and Concentration of Buffer on Capacity Factors

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Ion pairing in solutions of sodium tetraphenylborate

Conductance data are presented for sodium tetraphenylborate (NaBPh₄) in three solvent systems: water-dimethyl sulfoxide, water-acetone, and acetone-dimethyl sulfoxide. These and other data from the literature were first analyzed by the three-parameter equation Λ^′=Λ₀+Aτ²+Bτ³, where $$\Lambda \prime = [\Lambda (obs.) + \beta _0 c^{1/2} (1 + 0.5\tau ln 2\tau )]/[1 - \alpha _0 c^{1/2} + (\tau ^2 /3) ln 2\tau ]$$ Here, β₀ is the Onsager electrophoresis coefficient, α_oc^1/2 the limiting relaxation term, τ=e²κ/2DkT, κ^?1 is the Debye-Hückel distance, andA andB are empirical constants. The fact that three parameters are necessary to reproduce the data shows that ion pairing is not negligible for NaBPh₄ solutions despite the fact that the conductance curve lies above the limiting tangent even in ethanol (D=24.30). The quantity Λ_o is the limit of Λ^′ at zero concentration; the sum Aτ²+Bτ³ represents the part of the observed conductance from which the pairing constantK _Λ and the distance parameterR are derived. Conductance experiments should therefore be designed so that this sum is as large as possible, subject to the restriction that the highest concentration should not exceed 10^?7D³ (where the effects of short-range three-ion interactions are no longer negligible). Pairing constants for NaBPh₄ in the various solvents range from 4.6 in water to 70 in a mixture of Me₂SO and Me₂CO with dielectric constantD=23.80. The dependence ofE _s (the difference in free energy between solvent-separated pairs and contact pairs) on solvent composition is different for aprotic solvents and for mixtures containing water; for the latter, theE _s/kT vs. l/D plot shows a maximum while for the former the curve is monotone descending. The Walden produces (Λ_oη=limiting conductance times viscosity) plotted againstD ^?1 follow the same pattern.     

The molecular weight distribution for chain polymerization plus side reaction

The kinetics of chain polymerization is investigated for the case of a complicating side reaction. In addition to the polymerization reaction, A_i + M → A_i+1, there is a reversible side reaction, A_i + Q ↔ B_i. Initiation is assumed to be instantaneous. The monomer concentration M, and the concentration of the reacting species Q, are assumed to be constant. The reaction kinetics are solved exactly, yielding the distribution of living and dormant polymer, as well as the molecular weight distribution, as explicit functions of the reaction rate constants and the time. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1711–1725, 1997     

Concentration effects and thermodynamic nonideality in gel chromatography

The dependence of the elution volume V_e on the concentration of injected polymer c in gel chromatography is presented for several systems including poly(styrene) and poly(methyl methacrylate) in a number of pure solvents with SiO₂-based gels. The linear dependence of V_e on c and K_av on c (where K_av is the distribution coefficient) is confirmed in the region of very low concentration. The slopes k of the straight lines increase with increasing relative molecular masses M of the polymer injected and with increasing thermodynamic nonideality of the system (as expressed by the second virial coefficient A₂). The significance of the slope of the GPC calibration curve for meaningful comparison of the concentration effects in various chromatographic systems is pointed out. A recently found correlation between k and (A₂M)γ is confirmed with a γ value of about 0.8. A possible theoretical explanation for the deviation of γ from unity is discussed. Finally, the influence of both the polymer concentration and the thermodynamic quality of the eluent on the resolution index of the chromatographic system is evaluated with the conclusion that thermodynamically poor solvents should be preferred for preparative GPC separations with very high loads.     

Concentration Dependence of Elution Volumes in size Exclusion Chromatography of Polymer Molecules. II. Poly(Methyl Methacrylate) in Ideal Solvent

Abstract

The concentration effects occurring in size exclusion chromatography of polymer molecules have been investigated for the case of elution of macromolecules in an ideal solvent. It is shown that increases in the elution volumes with polymer concentration are detectable with the high efficiency columns employed. The concentration dependence of elution volumes is much lower than that previously determined with good solvents. The main factor contributing to the shift of elution volumes seems to be the viscosity of the polymer solutions, but another effect appears also to be present. This latter effect possibly suggest that in semi-concentrated solutions of polymer molecules in ideal solvents a continuous contraction of the polymer chains occurs, below their unperturbed dimensions, similar to that happening when the temperature of ideal solutions is decreased. More investigation on this point is needed. the ideal solutions is increased. Further investigations will be carried out to clarify this point.

In conclusion, the concentration dependence of polymer elution volumes in SEC has been found to be detectable also in a thermodynamically ideal solvent, though it is much lower than that observed in good solvents. In such a system, the main cause of the shift of elution volumes appears to be the viscosity of the polymer solutions, but a small additional contribution is also seen to be present. At the moment, it seems not possible to evaluate with certainty the origin of this latter contribution, especially in the absence of data on the macromolecular conformations in semi-concentrated solutions in ideal solvents.