Physical Chemistry of Polyelectrolyte Solutions, Volume 158 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Advances in Chemical Physics
• Sprache: Englisch

Seitenzahl: 423

Veröffentlichungsjahr: 2015

Beschreibung

The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This volume explores topics from Thermodynamic Properties of Polyelectrolyte Solutions to ion-binding of polyelectrolytes. The book features: * The only series of volumes available that presents the cutting edge of research in chemical physics * Contributions from experts in this field of research * Representative cross-section of research that questions established thinking on chemical solutions * An editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry or chemical physics

Leseprobe

Table of Contents

Cover

Editorial Board

Title Page

Copyright

Preface to the Series

Preface

Chapter 1: Introductory Remarks

I. Strong Electrolytes

II. Polymer Science

III. Polyelectrolyte Solutions

IV. (Supplement) Preparation of Linear Polymers with Narrow Molecular Weight Distribution (NMWD)

References

Chapter 2: Thermodynamic Properties of Polyelectrolyte Solutions

I. Introduction: Nonionic Polymer Solution

II. Electrostatic Free Energy of Polyelectrolyte Solutions

III. Donnan Membrane Equilibrium (Concentrated Solution)

IV. Dilute Solution Properties of Polyelectrolytes

V. (Appendix) Anomalous Osmosis of Water into Animal Cells

References

Chapter 3: Ionization Equilibrium and Potentiometric Titration of Weak Polyelectrolytes

I. Introduction

II. Theory of Ionization Equilibrium

III. Free Energy of Ionization in Solutions with Added-Salt

IV. Applications of Potentiometric Titration to The Study of Conformational Transition of Macromolecules

References

Chapter 4: Molecular Conformation of Linear Polyelectrolytes

I Introduction

II Unperturbed Dimension

III Stiffness of Polyion Backbone

References

Chapter 5: Radius of Gyration and Intrinsic Viscosity of Linear Polyelectrolytes

I. Introduction

II. Expansion Factor of Nonionic Polymer Coils Due to The Excluded Volume Effect

III. Expansion Factor of Polyelectrolyte Molecules in The Presence of Added-Salt

IV. Worm-Like Chain Model for []

V. In Pure Aqueous Solutions

References

Chapter 6: Transport Phenomena of Linear Polyelectrolytes

I. Introduction

II. Porous Sphere Model

III. Sedimentation and Diffusion

IV. Electrophoresis

V. Diffusion in Pure Aqueous Solution

VI. (Appendix) Anomalous Osmosis through Charged Membranes

References

Chapter 7: Ion-Binding

I. Introduction

II. Complex Formation

III. Ion-Pair in Simple Electrolyte Solutions

IV. Ion-Binding of Polyelectrolytes

References

Author Index

Subject Index

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Chapter 1: Introductory Remarks

Figure 1 Osmotic coefficient () versus degree of neutralization of PNaA () in pure aqueous solutions. Concn; 0.125 molar concentration of monomer. Degree of polymerization; 340. Temp. 20C. (Reproduced with permission from Ref. [6]. Copyright Wiley-VCH.)

Figure 2 Models of polyelectrolyte molecule.

Chapter 2: Thermodynamic Properties of Polyelectrolyte Solutions

Figure 1 Interpenetration function of poly(-methylstyrene) with narrow molecular weight distribution (NMWD) in good solvents. Solvents: (filled circles) cyclohexane; (open circles) trans-decalin; (cross in circles) toluene. Theoretical curves: FKO(o), Flory et al. [14]; FKO, modified by Stockmayer [15]; Yamakawa, [16]; S, Stockmayer [15]; CM-1 and -2, Casassa et al. [17]; KFSK, Kurata et al. [18]. (Reproduced with permission from Ref. [9]. Copyright American Chemical Society.)

Figure 2 Osmotic pressure () of poly(-methylstyrene) with different molecular weights in toluene at 25 C. Mol. wt. () from top to bottom); , , , , , , . (Reproduced with permission from Ref. [4]. Copyright American Chemical Society.)

Figure 3 Double-logarithmic plots of reduced osmotic pressure and degree of coil-overlapping (). The symbols are the same as in Figure 2. The full line and the broken curve denote eqs (15) and (12), respectively. (Reproduced with permission from Ref. [4]. Copyright American Chemical Society.)

Figure 4 Plots of against in semidilute region. The symbols are the same as in Figure 2. The solid curve denotes eq (16) with = 1.25. (Reproduced with permission from Ref. [4]. Copyright American Chemical Society.)

Figure 5 Crossover from semidilute solution to concentrated solution for osmotic pressure. The dotted and broken lines show the calculated values of eqs (6) and (16) for dilute and semidilute solutions, respectively. The solid lines show the calculated values of eq (18). The original paper should be referred to with respect to molecular weight and other details. (Reproduced with permission from Ref. [23]. Copyright American Chemical Society.)

Figure 6 Molecular weight–concentration diagram for three regions. D, S, and C denote dilute, semidilute, and concentrated solution regions, respectively. Sample; poly(styrene) with NMWD. Solvent, toluene or benzene. (Reproduced with permission from Ref. [23]. Copyright American Chemical Society.)

Figure 7 Mean activity coefficient of NaCl in polyelectrolyte solutions Polyelectrolyte sample; sodium poly(vinyl alcohol sulfate), deg. of polymerization , deg. of esterification 0.65. Curve 1, observed data; curve 2, calculated values of Katchalsky and Lifson eq (74) using from eq (70); curve 3, calculated values of Katchalsky and Lifson's theory using obtained from the data. (Reproduced with permission from Ref. [37]. Copyright Wiley.)

Figure 8 Donnan membrane potentials. Open circles denote observed values and broken lines denote calculated values of eqs (82). The solid lines denote the calculated values of eq (92) with activity coefficients of ions. The samples are the same as used in Figure 2. NaCl concentrations; A, 1.005 , E, 1.029 N. The data at three other salt concentrations in between A and E are similar to the aforementioned data. (Reproduced with permission from Ref. [42]. Copyright Wiley.)

Figure 9 (A) Reduced osmotic pressure versus polymer concentration (g/100 ml) for sodium pectinate in solutions of NaCl at 20 C. (B) The slope is the slope of the versus lines in Figure A. NaCl concentrations (mol/l) are indicated in the Figure (Reproduced with permission from Ref. [43]. Copyright Wiley.)

Figure 10 Plots of versus polymer concentration for sodium poly(styrene sulfonate) in aqueous NaCl solutions. Sample, fractionated, ; NaCl concentrations, (open circle) 0, (right-filled) 0.005; (upper-filled) 0.01; (cross) 0.02; (left-filled) 0.05; (down-filled) 0.1; (filled) 0.5 mol/l. , osmotic coefficient (see Section “Ion-binding of Polyelectrolytes”). The solid lines for salt-added systems denote the calculated values of eq (2) with in Figure 10 and (Reproduced with permission from Ref. [47]. Copyright American Chemical Society.)

Figure 11 Light scattering from polyelectrolyte solution in the presence of added-salt (NaCl). Sample, Sodium poly(styrenesulfonate). . NaCl concentrations from top to bottom, 0.005, 0.01, 0.02, 0.05, 0.1 mol/l. Temp., 25C. (Reproduced with permission from Ref. [45]. Copyright American Chemical Society.)

Figure 12 (A) Plots of second virial coefficients () versus reciprocal ionic strength. (B) versus reciprocal square root of ionic strength. Sample: NaPSS in NaCl solutions. (Open circles) (LS) from Figure 11, (crosses) (OS) from Figure 10. (Reproduced with permission from Ref. [47]. Copyright American Chemical Society.)

Figure 13 Dependence of on molecular weight. Sample and NaCl concentrations are the same as in Figure 11 (Reproduced with permission from Ref. [45]. Copyright American Chemical Society.)

Figure 14 Interpenetration function of a polyelectrolyte molecule in NaCl solutions. Polymer sample: fractionated poly(sodium styrenesulfonate) (NaPSS); of NaPSS (), (open circles) 22.8 0.5, (filled circles) 23.4 1.0, (bar in circle) 15.5 0.5, (dot in circle) 10.0 0.5; NaCl concentrations from 2 M to 0.005 M. Theories: Curve 1, Flory–Krigbaum–Orofino (original) [14], curve 2, Stockmayer [15], curve 3, Casassa–Markovitz [17]. Kurata et al.'s theory [18] gives almost the same results as Casassa–Markovitz. (Reproduced with permission from Ref. [45]. Copyright American Chemical Society.)

Figure 15 Schematic diagram of the half cell for measuring volume flux. Labels: b, magnetic stirrer bar; c, capillary tube; g, rubber gasket; m, membrane; s, magnetic stirrer; t, three-way stopcock. The effective area of the membrane is 3.14 cm. (Reproduced with permission from Ref. [56]. Copyright Elsevier.)

Figure 16 Transported volume per unit area of membrane against time. A, observed on the poly(oxyethylene)side; B, observed on the NaCl solution side. (Reproduced with permission from Ref. [56]. Copyright Elsevier.)

Chapter 3: Ionization Equilibrium and Potentiometric Titration of Weak Polyelectrolytes

Figure 1 Schematic explanation of surface of macro-ions.

Figure 2 Potentiometric titration curve of isoionic -lactoglobulin. NaCl concentration: 0.100 N. Protein concentration: 0.500%. (Reproduced with permission from Ref. [16]. Copyright American Chemical Society.)

Figure 3 Comparison between theoretical (solid curves) and experimental potentiometric titration data for the carboxyl groups of conalbumin. KCl concentration, temperature, and : (I) 0.100 mol/l, 25 C, Å and Å; (II) 0.03, 25 C, 32 Å and 1.8 Å; (III) 0.01, 25 C, 32 Å and 1 Å; (IV) 0.100, 5 C, 32 Å and 0.5 Å. Data quoted from Ref. [17]. (Reproduced with permission from Ref. [12]. Copyright American Chemical Society.)

Figure 4 Comparison between theoretical (solid line) and experimental values of potentiometric titration for various groups of conalbumin in 0.100 mol/l solution of KCl. Å is assumed. Group titrated: (I) phenolic; temperature, 25 C, Å. (II) phenolic; 22 C, 0 Å. (III) -amino; 25 C, 0.4 Å. (IV) phenolic; 5 C, 0.6 Å. (V) -amino; 5 C, 2.4 Å. Data quoted from Ref. [17]. (Reproduced with permission from Ref. [12]. Copyright American Chemical Society.)

Figure 5 Comparison between theoretical and experimental potentiometric titration curves for –COOH of bovine plasma albumin at NaCl concentration=0.15 mol/l. Protein concentration: (circles with tip facing up) 0.772 g/dl, (with tip facing down) 0.386, (with tip facing right) 0.154, (triangle) 0.538. (Reproduced with permission from Ref. [22]. Copyright Elsevier.)

Figure 6 Comparison between theoretical and experimental potentiometric titration curves for –COOH of bovine plasma albumin at lower ionic strengths. NaCl concentrations: 0.01 mol/l (I, II) (filled) and 0.03 (III, IV)(half-filled). Polymer concentrations: (filled circles with tip facing up) 0.772 g/dl, (filled with tip facing down) 0.386 and (filled with tip to the right) 0.154, (half-filled circles with tip facing up) 0.772, and (half-filled with tip to the right) 0.386. Two pairs of theoretical curves, I and III, II and IV calculated for = 32 and 40 Å, respectively. (Reproduced with permission from Ref. [22]. Copyright Elsevier.)

Figure 7 Comparison between theoretical (rod) and experimental potentiometric titration curves of carboxymethyl cellulose. NaCl concentrations from top to bottom: 0.0100, 0.0200, 0.0500, 0.100, and 0.200 mol/l. Polymer concentrations: 0.0084–0.0044 base mol/l. The solid lines denote the calculated values for a rod with Å. The ionic strength dependence of in Table I is taken into account in the calculation. (Reproduced with permission from Ref. [3]. Copyright Wiley.)

Figure 8 Comparison between theoretical (rod) and experimental potentiometric titration curves of stereoregular poly(methacrylic acids). The open, filled, and half-filled circles denote the data for isotactic, atactic, and syndiotactic poly(methacrylic acid)s, respectively. NaCl concentrations: (A) 0.0100 and (B) 0.100 mol/l. Thin solid lines denote the data extrapolated to infinite dilution. Polymer concentrations: 0.0084–0.0044 base mol/l. Thick solid lines denote the calculated values for rod assuming = 5.5 Å. is assumed to be 3.37, and the ionic strength dependence of in Table I is taken into account in calculation. (Reproduced with permission from Ref. [28]. Copyright American Chemical Society.)

Figure 9 (A) Comparison between theoretical (rod) and experimental potentiometric titration curves of poly(acrylic acid). Circles show the experimental data at the lowest concentration of the sample (0.00829 N). Thin solid lines are the experimental values extrapolated to infinite dilution. Thick solid lines denote the calculated rod values. Concentration of added-salt (NaCl): (1) 5.00; (2) 1.00; (3) 2.00; (4) 5.00; 5, 1.00 N. (B) The same data replotted in the form of versus at constant degrees of neutralization () Solid lines denote the calculated values assuming cm. (Reproduced with permission from Ref. [28]. Copyright American Chemical Society.)

Figure 10 Comparison between theoretical (rod) and experimental potentiometric titration data of a random copolymer of d- and l-glutamic acids. Dotted lines denote the data of Olander and Holtzer [33]. Solid lines are the calculated rod values, assuming Å. NaCl concentrations from top to bottom: 0.01, 0.05, 0.10, and 0.40 M . The value of at 0.4 M of NaCl is assumed arbitrarily. (Reproduced with permission from Ref. [3]. Copyright Wiley.)

Figure 11 Potentiometric titration curves of poly(l-glutamic acid). (I) NaCl concentration, 0.00500 mol/l; polym. concentration, 0.0188 base mol/l. (II) 0.0200, 0.0188. (III) 0.0200, 0.0342. (IV) 0.200, 0.0188. Regions A, B, C, and D are explained in the text. (Reproduced with permission from Ref. [35]. Copyright ACS.)

Figure 12 Comparison between theoretical (rod) and experimental potentiometric titration curves of poly(d-glutamic acid) in the helical region NaCl concentrations: 0.0100, 0.0200, 0.0500, 0.100, and 0.200 mol/l from top to bottom. Polymer concentrations: filled circles 0.002–0.003 base mol/l; open circles 0.001. The solid and broken lines denote the calculated values assuming and 9.0 Å, respectively. (Reproduced with permission from Ref. [3]. Copyright Wiley.)

Figure 13 Modified Henderson–Hasselbalch plots of poly(methacrylic acid) (circles) and poly(acrylic acid) (squares) in pure aqueous solutions. Concentrations: (circles) base mol/l and (squares) . (Reproduced with permission from Ref. [43]. Copyright Wiley.)

Figure 14 Method for determining the degree of helix. Experimental points are for a solution of 0.0500 M NaCl and 0.0188 N PGA. Horizontal arrows in B represent solutions in which = 3 (bottom), 1 (middle) and 1/3 (top). (Reproduced with permission from Ref. [35]. Copyright ACS.)

Figure 15 A method of determining from a potentiometric titration curve. Poly(l-glutamic acid) in 0.0100 M NaCl. The shaded area for gives . (Reproduced with permission from Ref. [35]. Copyright ACS.)

Figure 16 Relationship between of optical rotatory dispersion and degree of helix from titration. Data for 0.341% PGA in 0.200 M NaCl. (Reproduced with permission from Ref. [35]. Copyright ACS.)

Figure 17 Fraction of residues in helical regions as a function of fraction of carboxyls ionized, for poly(l-glutamic acid).At room temperature, in 0.20 M NaCl. (open circles) helix content determined by extinction coefficients and (open and filled squares) by potentiometric titration. (Reproduced with permission from Ref. [33]. Copyright ACS.)

Figure 18 Standard free energy change for taking uncharged residues from random coil to helix as a function of leucine composition in the helix–coil transition of copolymers of leucine and glutamic acid. (Reproduced with permission from Ref. [46]. Copyright ACS.)

Figure 19 Dependence of on concentration of NaCl.Filled circle is for a solution 0.0342 N in PGA; others are 0.0188 N PGA. (Reproduced with permission from Ref. [35]. Copyright ACS.)

Figure 20 Titration curves of poly(l-glutamic acid) in 0.10 M NaCl at various temperatures.Extrapolations are shown for the 0.6 titration. (Reproduced with permission from Ref. [33]. Copyright ACS.)

Figure 21 Free-energy change per residue of the uncharged helix–uncharged coil transition as a function of temperature at various salt concentrations.Solid line is the linear least-squares fit of all data. (Reproduced with permission from Ref. [33]. Copyright ACS.)

Figure 22 Theoretical and experimental curves of versus

Z

for the carboxyl groups of -lactoglobulin in 0.5 and 0.01 M NaCl solutions.Circles denote experimental points for 0.194% protein and filled circles for 0.469% in 0.01 M NaCl. Dashed curves OP'PA and OQQ'B are calculated from theory for dimer and subunit in 0.01 M NaCl with Å and 26.2/2 Å, assuming Å. Solid lines 1 and 2 are those calculated for mixtures of dimer and subunits using the dashed curves as a basis. Squares are data points for 0.469% protein in 0.5 M NaCl. Theoretical curves O'C and O'D are calculated with Å, assuming and 1.2 Å, respectively. (Reproduced with permission from Ref. [16]. Copyright ACS.)

Chapter 4: Molecular Conformation of Linear Polyelectrolytes

Figure 1 A schematic diagram of a typical vinyl polymer chain. Side group X is COOH for poly(acrylic acid). The energy map is given for the transform of chain(2) against chain(1).

Figure 2 Double logarithmic plots of intrinsic viscosity versus molecular weight of polyelectrolytes at states. (A) Poly(sodium or potassium vinyl sulfonate). The numbers correspond to the numbers in Table I. is the degree of polymerization. (Reproduced with permission from Ref. [12]. Copyright AIP.) (B) Poly(sodium acrylate). (Half-filled circles) 1.5 N NaBr; (open circles) 1.25 N NaSCN, (see, Table I). (Reproduced from with permission from Ref. [11]. Copyright Chemical Society of Japan.)

Figure 3 Square-root plots of () at various scattering angles in light scattering from polyelectrolyte solutions. Sample, poly(sodium acrylate) () with narrow molecular weight distribution (NMWD) in aqueous solution of 0.1 NaBr (-temperature). (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 4 Comparison between Debye's theory eq (18) in the Introductory Remarks and the experimental of a polyelectrolyte with NMWD at a state. Sample, poly(sodium acrylate) with NMWD () in aqueous solution of 1.5 N NaBr at C ( temperature). The solid curve shows the calculated values of eq (18) in the Introductory Remarks, assuming = 630 Å. The initial slope, shown by a broken line, is drawn by using the value of . (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 5 Comparison of experimental with Peterlin's theory at different and constant degree of neutralization (0.2). The solid lines are calculated from Peterlin's theory, eq (21), using (from top to bottom) = 1620 Å and = 0.30 (0.28) in = 0.01 N; = 1300 Å and = 0.25 (0.23) in = 0.025 N; and = 850 Å and = 0.05 (0.02) in = 0.5 N. The values of in parenthesis are estimated from eq (19). Broken lines show Debye's theory, eq (18) in the Introductory Remarks. (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 6 Comparison of experimental with Peterlin's theory at different degrees of neutralization and constant (0.025 N). The solid lines are calculated from Peterlin'S theory, eq (21), using = 1390 Å, = 0.30 (0.28) at = 0.4; = 1300 Å, = 0.25 (0.23) at = 0.2; and = 1230 Å, = 0.20 (0.19) at = 0.1. The values of in parenthesis are estimated from eq (19). (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 7 Comparison of for various conformations using the same value of = 1630 Å at and N. The broken line shows the initial slope. The solid line (D) is calculated from Debye's theory, eq (18) in the Introductory Remarks; (SB) Sharp and Bloomfield, eq (28) using = 210 Å; (P) Peterlin, eq (21) using = 0.30 (0.24); and for rod (R) eq (31). The values of in parenthesis are estimated from eq (19). (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 8 Experimental of three poly(styrene)s with high molecular weights and NMWD plotted against . The half-filled circles, open circles with bar and open circles denote the data for the samples with , and , respectively. The solid lines D and P show the calculated values of eq (18) in Introductory Remarks and (21), respectively. The broken line shows the calculated values of eq (23) assuming

Z

= 0.05. (Reproduced with permission from Ref. [24]. Copyright ACS.)

Figure 9 Expansion factor of parts of polymer chain. Estimated from the data in Figure 8 (Reproduced with permission from Ref. [26]. Copyright Elsevier.)

Figure 10 Comparison between experimental of PTBC and Sharp and Bloomfield's theory. Sample; PTBC with NMWD, . Solvent;

n

-butyl chloride. The curves denote the theoretical for a worm-like chain. (A) Å, 1/(2) = 75 Å, (B) Å, = 65 Å, (C) Å, 1/(2) = 60, 55, and 50 Å, from top to bottom. (Reproduced with permission from Ref. [39]. Copyright ACS.)

Figure 11 Comparison between of poly(sodium acrylate) with NMWD () and a theory for worm-like chains, eq (28). NaBr concentration = 0.025 N. Å is assumed. The values of 1/(2) and the values of calculated from 1/(2) using eq (30) are shown in the Figure (Reproduced with permission from Ref. [15]. Copyright ACS.)

Figure 12 Schematic illustration of Kratky plot for flexible linear polymer.

Figure 13 Kratky plot for poly(

t

-butyl acrylate) in toluene. The polymer concentrations are 6.6 and 2.2%(w/v) from top to bottom. (Reproduced with permission from Ref. [31]. Copyright ACS.)

Figure 14 Kratky plots for (A) poly(

t

-butyl methacrylate) and (B) poly(

t

-butyl crotonate) (stiff) in toluene. The polymer concentrations are (A) 5.0 and 3.3, (B) 4.8, 2.4 and 1.2% (w/v) from top to bottom. (Reproduced with permission from Ref. [31]. Copyright ACS.)

Figure 15 Comparison between the Kratky plots of poly(acrylic acid) (open circles) and poly(sodium acrylate) (circles with tip). P(AA) (open circles): degree of neutralization , concentration of NaCl , polymer concentration g/dl. P(NaA) (circles with tip): , N, g/dl. (Reproduced with permission from Ref. [43]. Copyright ACS.)

Figure 16 Kratky plot for sodium poly(acrylate). (A) At high ionic strengths. (, N, = 3.2, 1.6 g/dl). (B) At low ionic strengths. (, M, g/dl; , M, g/dl; , M, g/dl.) from top to bottom. (Reproduced with permission from Ref. [43]. Copyright ACS.)

Figure 17 Kratky plots of isotactic (lower) and syndiotactic (upper) poly(methyl methacrylates) (PMMA) Polymer concentrations are 12 and 9 g/dl, respectively. (Reproduced with permission from Ref. [46]. Copyright ACS.)

Figure 18 Comparison between the Kratky plots of syndiotactic poly(methyl methacrylate) in acetone (filled circles) and syndiotactic poly(sodium methacrylate) with (open circles). Polymer concentration, 9 and 17 g/dl, respectively.(Reproduced with permission from Ref. [46]. Copyright ACS.)

Figure 19 Three conformers of poly(sodium acrylate) and its model compound. Capital C denotes the preceding and succeeding polymer chains for poly(sodium acrylate), and denotes the methyl groups for

meso

-DMGA. X denotes COOH. (Reproduced with permission from Ref. [50]. Copyright ACS.)

Figure 20 Methylene spectra of

meso

-DMGA and its sodium salts. (A) observed spectrum of

meso

-DMGA ( in octadeuteriodioxane-O), (B)–(D) observed spectra of

meso

-NaDMGA with degree of neutralization of (B) 0.25, (B) 0.50, and (D) 1.00 in O; (A') and (D') are calculated spectra obtained with parameters for (A) and (D) in Table V, respectively. (Reproduced with permission from Ref. [50]. Copyright ACS.)

Figure 21 NMR spectra of isotactic poly(methyl acrylate) and isotactic poly(sodium acrylate). (A) Observed methylene and methine spectra of isotactic P(MA) in

o

-dichlorobenzene at 115 C; (B)–(D) observed methylene spectra of isotactic P(NaA) with degree of neutralization (DN) of (B) 0.20, (C) 0.50, and (D) 1.00 in O at 100 C; (E) observed methylene spectrum of isotactic P(NaA) with DN of 100% in O with 0.5 M NaCl at 100 C; (B')–(D') calculated methylene spectra obtained with parameters for (b)–(d) in Table VI, respectively. Concentrations are 10% (w/v) for all samples. (Reproduced with permission from Ref. [50]. Copyright ACS.)

Chapter 5: Radius of Gyration and Intrinsic Viscosity of Linear Polyelectrolytes

Figure 1 A typical example of viscosity behavior of polyelectrolyte solution (by Fujita and Homma). Sample, sodium carboxymethyl cellulose (degree of polymerization, 417); Concentrations of added-salt (NaCl) (mol/l) are denoted in the figure; Temperature, 25 C. (Reproduced with permission from Ref. [14]. Copyright Wiley.)

Figure 2 Double logarithmic plots of intrinsic viscosity versus molecular weight relationship of poly(sodium acrylate) in sodium bromide solution at C. Ionic strength of NaBr from bottom to top: and, . (Reproduced with permission from Ref. [3]. Copyright ACS.)

Figure 3 An example of Stockmayer–Fixman–Kurata plot for of nonionic polymers from Inagaki et al. [19]. Sample; poly(styrene). Solvents: (filled circle) benzene at 30 C (good solvent), (half-filled circle) methyl-ethyl-ketone at 22 C (poor solvent), (open circle) cyclohexane at 34.5 C ( solvent). (Reproduced with permission from Ref. [12]. Copyright Asakura Shoten.)

Figure 4 Plots of versus (open circles) and versus (filled circles), determined by light scattering. Sample, poly(-methyl styrene) with NMWD in toluene at C. Crossed out circles denote from Berry for polystyrene with NMWD (see the original paper [22]). (Reproduced with permission from Ref. [26]. Copyright ACS.)

Figure 5 Plots of versus for poly(-methyl styrene) with NMWD in toluene and in

t

-decalin at various temperatures. Expansion factors were calculated from . Circles with bar denote the data in toluene, while open circles with tip show the data in

t

-decalin at , and C, from top to bottom. Half-filled circles show the data from Cowie et al. in toluene at C [28]. (Reproduced with permission from Ref. [27]. Copyright ACS.)

Figure 6 Flory, Fox, and Schaefgen's plots of of poly(sodium acrylate) in NaBr solution. Concentrations of NaBr and experimental conditions are the same as in Figure 2. (Reproduced with permission from Ref. [3]. Copyright ACS.)

Figure 7 Stockmayer, Fixman, and Kurata's plots of of poly(sodium acrylate) in NaBr solution. Data are the same as in Figure 6. (Reproduced with permission from Ref. [3]. Copyright ACS.)

Figure 8

B

versus plot. Symbols circles and diamonds denote the values determined from the theories in Refs [16] and [17], respectively. (Reproduced with permission from Ref. [3]. Copyright ACS.)

Figure 9 Typical examples of the relationship between intrinsic viscosity () and degree of neutralization () Concentrations of NaBr, 0.1 N; Solid lines denote the data of PAA with (top) and (bottom). Broken lines denote the data of PMAA with (top) and (bottom). (Reproduced with permission from Ref. [4]. Copyright ACS.)

Figure 10 Plot of the electrostatic expansion factor versus of poly(sodium acrylate) in NaBr solution. Concentration of NaBr from top to bottom; 0.5, 0.1, 0.025, and 0.01 N. at C. Degree of neutralization, ; (A) 0.103, (B) 0.600. Solid lines 1 and 2 denote the calculated values of eqs (52) and (57), respectively. (Reproduced with permission from Ref. [4]. Copyright ACS.)

Figure 11 Plot of the electrostatic expansion factor versus of poly(sodium acrylate) in NaBr solution. Concentration of NaBr, temperature and degree of neutralization, are the same as in Figure 10. Solid line 3 denotes the calculated values of eq (53). (Reproduced with permission from Ref. [4]. Copyright ACS.)

Figure 12 Plot of electrostatic expansion factor versus of poly(sodium acrylate) with high molecular weights in NaBr solution. of the samples; , and . Degree of neutralization (); 0.2. The data are plotted together with the data obtained in Figure 11. (Reproduced with permission from Ref. [40]. Copyright The Society of Polymer Science Japan.)

Figure 13 Plot of versus of poly(sodium acrylate) with high molecular weights in NaBr solution Data are the same as in Figure 34. (Reproduced with permission from Ref. [40]. Copyright The Society of Polymer Science Japan.)

Figure 14 Double logarithmic plots of intrinsic viscosity versus weight–average molecular weights of PTBC. (Open circles with tip facing up) observed values in toluene, (tip-right) in ethyl acetate, (tip-left) values at a state estimated from the data on toluene, (tip-down) values at a state estimated from the data on ethyl acetate. The full, broken, and chain lines denote experimental (), theoretical ( = 60 Å, 1/(2) = 55 Å, d = 5.5 Å), and theoretical ( = 60 Å, 1/(2) = 50 Å, Å), respectively. (Reproduced with permission from Ref. [46]. Copyright ACS.)

Figure 15 Molecular weight (

M

) dependence of of poly(sodium acrylate) samples at

i

= 1.0. Sample: the sample used is the same as in Section “Stiffness of Polyion Backbone”. Concentrations of added NaBr () are given in the Figure Theoretical curves for worm-like chains, eq (64), are depicted by solid lines for Å and by broken lines for Å. = 40 Å. The persistence length is assumed to be 100 and 90 Å in N, respectively, for the assumption of and 5 Å; 70 and 60 Å in 0.025 N; 40 and 35 Å in 0.1 N; 22 and 20 Å in 1.5 N. (Reproduced with permission from Ref. [48]. Copyright ACS.)

Figure 16 Added-salt concentration dependence of the persistence length

of poly(sodium acrylate) (

). The open and filled circles show the values obtained for

and 5 Å, respectively. (Reproduced with permission from Ref. [48]. Copyright ACS.)

Figure 17 (A) Plots of the three scattering curves versus . (B) Scattering function as a function of for two values. Symbols in Figure are different from the symbols in the text; (A) , (B) and . Polymer concentrations is 0.338

M

. (Reproduced with permission from Ref. [50]. Copyright Springer.)

Chapter 6: Transport Phenomena of Linear Polyelectrolytes

Figure 1 A porous sphere with uniform distribution of fixed charges.

Figure 2 Electrostatic potential distributions calculated from various theories. It is assumed that = 1070 and cm. Curve 1 shows the calculated values of eqs (5) and (6), 2; by Kimball et al. [8], 4; eqs (19) and (20), 5; eqs (21) and (22). Referred to [9] in regard to the others. (Reproduced with permission from Ref. [9]. Copyright Chem. Society of Japan.)

Figure 3 Charge distribution on both sides of the surface of the porous sphere. (1) ; (2) ; (3) , (4) the Donnan–Helmholtz model. (Reproduced with permission from Ref. [9]. Copyright Chem. Society of Japan)

Figure 4 Polymer concentration dependence of the sedimentation coefficient of poly(sodium styrene sulfonate) in NaCl solution. Samples, open circles; No. 7 (); filled circles, No. 2 (); NaCl concentrations, 1, 0.005; 2, 0.01; 3, 0.02; 4, 0.05; 5, 0.2 (N). Speed of rotation, 59,780 rpm. (Reproduced from Ref. [20]. Copyright ACS.)

Figure 5 Ionic strength dependence of Mandelkern–Flory's coefficient. The samples are the same as in Figure 4. () from top to bottom, No. 9 (0.39); No. 8 (0.49); No. 7 (1.0); No. 6 (1.2; No. 5 (1.5); No. 4 (2.1)); No. 2 (2.3). denote the values calculated from . (Reproduced with permission from Ref. [20]. Copyright ACS.)

Figure 6 Plots of versus . Samples; filled circles, No. 2 (; open circles, No. 4 . The broken line denotes the calculated values of eq (46) assuming Å. (Reproduced with permission from Ref. [20]. Copyright ACS.)

Figure 7 Polymer concentration dependence of diffusion coefficient of poly(sodium styrene sulfonate) in NaCl solution. Sample: No. 8 of the same samples in Figure 8. NaCl concentrations (from bottom to top): 0.2, 0.05, 0.02, 0.01, and 0.005 N. (Reproduced with permission from Ref. [21]. Copyright ACS.)

Figure 8 Added-salt concentration dependence of (filled circles) and (open circles). (Reproduced with permission from Ref. [21]. Copyright ACS.)

Figure 9 A schematic diagram of a moving boundary cell. The polyion is assumed to have the negative charges. The letters a and b show the initial boundaries. The dark area shows sample solution, while the upper white area denotes solvent. The boundary a ascends toward the cathode, whereas b descends

Figure 10 Polymer concentration dependence of from ascending (filled circles) and descending (open circles) boundaries. Sample, poly(sodium vinyl alcohol sulfate); degree of polymerization, 1600; degree of esterification, 0.61. NaCl concentrations (A) 0.05 N, (B) 0.005 N. (Reproduced with permission from Ref. [25]. Copyright Wiley.)

Figure 11 Dependence of on added-salt (NaCl) concentration. The sample is the same as in Figure 10. The broken line shows calculated values of eq (69) (Reproduced with permission from Ref. [25]. Copyright Wiley.)

Figure 12 Molecular weight dependence of of poly(sodium acrylate) with different degrees of neutralization at a high ionic strength. Degree of neutralization from top to bottom, 1.0 (open circles), 0.6, 0.4, 0.2 (filled circles), 0.1, 0.05. Solid lines 1 and 2 are the calculated values for the solid sphere model by using Henry's theory (see text). (Reproduced with permission from Ref. [26]. Copyright ACS.)

Figure 13 Determining the charge density distribution of carboxymethyl cellulose (CMC). Filled circles are the expected values, Open circles are the observed values of a mixture of two samples. (Reproduced with permission from Ref. [29]. Copyright Soc. Polymer Sci. Japan.)

Figure 13 Determining the charge density distribution of carboxymethyl cellulose (CMC). Filled circles are the expected values, Open circles are the observed values of a mixture of two samples. (Reproduced with permission from Ref. [29]. Copyright Soc. Polymer Sci. Japan.)

Figure 14 The creation of a diffusion front in schlieren patterns (by Spinco model H). (Left) Na-PSS: Concentrations of monomer, 0.0793 N (298 fringes). Time, 5400, 21,600, 43,200 s (from the top). (Right) H-PSS: Concentrations of monomer, 0.793 N. Time, 3960, 7560, 11,160 s (from the top) (Reproduced with permission from Ref. [31]. Copyright ACS.)

Figure 15 Diffusion fronts of (A) Na-PSS ( s) and (B) H-PSS ( s). Upper photos are schlieren patterns and lower photos are Rayleigh patterns (by Spinco model H). Concentrations are the same as in Figure 14. (Reproduced from Ref. [31]. Copyright ACS.)

Figure 16 Moving velocities of diffusion front (). Sample, Na-PSS, concentrations, (1) 141.4, (2) 96.6, (3) 58.6, (4) 28.7 fringes, from top to bottom. (Reproduced from Ref. [31]. Copyright ACS.)

Figure 17 Concentration dependence of the diffusion coefficient. (A) Average diffusion coefficient. (B) Via the Boltzmann–Matano method. (1) and (top), H-PSS. (2) and (bottom), Na-PSS. Numbers indicate concentrations by fringe numbers. (Reproduced with permission from Ref. [31]. Copyright ACS.)

Figure 18 An apparatus for measuring the osmotic flow of water. B, bottle for adjusting the head difference; C, cooler; CT, capillary tube; E, electrode for conductivity measurements; F, feeding bottle; M, membrane; MS, magnetic stirrer; S, stirrer; T, magnetic stirrer tip. (Reproduced with permission from Ref. [42]. Copyright ACS.)

Figure 19 Flow of KCl solution through membranes C-1 (with a lower charge density) and C-2 (with a higher charge density) Concentration ratio of KCl (); Membrane (C-1) A, 2; B, 4; C, 8; D,16. Membrane (C-2) E, 2; F, 4; G, 8. (Reproduced with permission from Ref. [42]. Copyright ACS.)

Figure 20 The dependence of on concentrations of various electrolytes. Membrane C-1. (A) (open circles) =2: tip up, KCl; tip right, NaCl; tip left, LiCl. (B) (right-filled circles) = 4: tip up, KCl; tip right, NaCl; tip left, LiCl. (C) (left-filled circles) = 8: tip up, KCl; tip right, NaCl; tip left, LiCl. (D) (filled circles) = 16: KCl. (A) (open circles with tip down) denotes the dependence of on KCl concentrations at = 2. (Reproduced with permission from Ref. [42]. Copyright ACS.)

Chapter 7: Ion-Binding

Figure 1 Titration curves of poly(methacrylic acid) solution with sodium hydroxide in addition of Cu(. equiv/l. Concentrations of Cu(: (1) 0, (2) , (3) , (4) , (5) M. (Reproduced with permission from Ref. [13]. Copyright Wiley.)

Figure 2 Dependence of activity coefficient on sample concentration (equivalent concentration of ). Sample, Na-PVS. Deg. of est.: (1) 0.726, (2) 0.692, (3) 0.740, (4) 0.711, (5) 0.494, (6) 0.431, and (7) 0.301. (Reproduced with permission from Ref. [38]. Copyright Wiley.)

Figure 3 Dependence of activity coefficient on the distance between the neighboring charged groups at 0.0100 N. Samples, (open circles) Na-PVS in Figure 2, (left-filled) Na-CMC, (bottom filled) Na-CS. (filled) and (right filled) in Ag-CMC sol. [40]. (Reproduced with permission from Ref. [38]. Copyright Wiley.)

Figure 4 Osmotic coefficient versus polymer concentration for Na-PSS in pure aqueous solution. Sample, sodium poly(styrene sulfonate) (Reproduced with permission from Ref. [44]. Copyright ACS.)

Figure 5 Electric mobilities of () and polyion () in pure aqueous solution of Na-PVS. (Reproduced with permission from Ref. [45]. Copyright Chemical Society of Japan.)

Figure 6 Dependence of the ionic activity coefficient of on equivalent concentration of Na-PVS in solutions of various concentrations of NaCl. NaCl concentrations: (A) , (B) , (C) , (D) , (E) , (F) , (G) in pure aqueous solution as in Figure 2 (Reproduced with permission from Ref. [46]. Copyright Wiley.)

Figure 7 Dependence of the ionic activity coefficient of on equivalent concentration of Na-PVS in solutions of various concentration of NaCl. NaCl concentrations are the same as in Figure 6 (Reproduced with permission from Ref. [46]. Copyright Wiley.)

Figure 8 Cell for transference experiments A, anode; B, middle; C, cathode. (Reproduced with permission from Ref. [49]. Copyright ACS.)

Figure 9 Degree of counter-ion association () versus degree of neutralization . (A) (by Huizenga et al. [47]), Sample, sodium poly(acrylate) in pure aqueous solution. Polymer concentrations: (filled circles) 0.0151 N, (open circles) 0.0378 N. (B) (by Nagasawa et al. [49]); Sample, sodium poly(acrylate) in NaCl solutions. Polymer concentrations: 0.04309 N. NaCl concentrations: (open circles) 0.0982 N, (filled circles) 0.0491, (half filled circles) 0.00982 N, (cross) in pure aqueous solution by Huizenga et al. (Reproduced with permission from Refs [47, 49]. Copyright ACS.)

Figure 10 Chemical shifts of proton in aqueous solution of poly(styrene sulfonic acid) (Reproduced with permission from Ref. [67]. Copyright ACS.)

Figure 11 Conductometric titrations of poly(vinylsulfonic acid) with LiOH, NaOH, KOH, and at . (Reproduced with permission from Ref. [68]. Copyright ACS.)

Figure 12 Calculated values of versus distance from the polyion axis.. Diameter of the rod, = 5.66 Å. Concentrations of added-salt corresponding to a/ = 0.9, 0.4, 0.2, and 0.04 are 0.465, 0.0918, 0.0230, and 0.000918 M, respectively. The broken lines denote the calculated values of linearized solution. (Reproduced with permission from Ref. [69]. Copyright AIP Publishing LLC.)

Figure 13 Concentration of excess counter-ions versus distance from polyion axis.

C

is the bulk concentration of added-salt. Parameters are described in Figure 12. (Reproduced with permission from Ref. [69]. Copyright AIP Publishing LLC.)

Figure 14 versus distance from the polyion axis. Parameters are described in Figure 12. The straight lines from the origin indicate the corresponding asymptotic curves. (Reproduced with permission from Ref. [69]. Copyright AIP Publishing LLC.)

List of Tables

Chapter 3: Ionization Equilibrium and Potentiometric Titration of Weak Polyelectrolytes

Table I Activity Coefficient of a Fixed Group on Linear Polyelectrolytes [3]

Table II TitraTable Amino Acid per Mole (35,500) of -lactoglobulin [15]

Table III Nonelectric Part of the Standard Free-Energy Change for the Helix–Coil Transition of Polypeptides [9]

Table IV (kcal/ru) of -Lactoglobulin [16]

Table V (kcal/ru) of -Lactoglobulin by the “Area” Method from Data for 0.01 M NaCl [16]

Chapter 4: Molecular Conformation of Linear Polyelectrolytes

Table I Examples of Solvents for Polyelectrolytes

Table II Molecular Characteristics of Deuterium-Labeled Polystyrenes [29]

Table III Radii of Gyration and Expansion Factors of Deuterated Parts [29]

Table IV Dependence of Persistence Length () of Poly(sodium acrylate) on Degree of Neutralization () and Concentration of NaCl()

Table V Relative Chemical Shifts and Spin-Coupling Constants (in cps) of -Protons of Sodium --Dimethylglutarate

Table VI Relative Chemical Shifts and Spin-Coupling Constants (in cps) of -Protons of Isotactic Poly(sodium acrylate)

Table VII Conformations of Sodium --Dimethylglutarate and Isotactic Poly(sodium acrylate)

Chapter 6: Transport Phenomena of Linear Polyelectrolytes

Table I and Mandelkern–Flory's Coefficients

Table II Comparison Between and Second Virial Coefficient

Table III Electrophoretic Mobilities of Various Salts of Poly(styrene sulfonic acid) [27]. Added-salt concentrations; 0.100 N

Table IV Moving Velocity of the Diffusion Front of H-PSS [31]

Table V Examples of

Chapter 7: Ion-Binding

Table I Mobilities of the Polyion, Counter-ion, and By-ion of Poly(sodium acrylate)

Editorial Board

Kurt Binder, Condensed Matter Theory Group, Institut Für Physik, Johannes Gutenberg-Universität, Mainz, Germany

William T. Coffey, Department of Electronic and Electrical Engineering, Printing House, Trinity College, Dublin, Ireland

Karl F. Freed, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois USA

Daan Frenkel, Department of Chemistry, Trinity College, University of Cambridge, Cambridge, United Kingdom

Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium

Martin Gruebele, Departments of Physics and Chemistry, Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois USA

Gerhard Hummer, Theoretical Biophysics Section, NIDDK-National Institutes of Health, Bethesda, Maryland USA

Ronnie Kosloff, Department of Physical Chemistry, Institute of Chemistry and Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel

Ka Yee Lee, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois USA

Todd J. Martinez, Department of Chemistry, Photon Science, Stanford University, Stanford, California USA

Shaul Mukamel, Department of Chemistry, School of Physical Sciences, University of California, Irvine, California USA

Jose N. Onuchic, Department of Physics, Center for Theoretical Biological Physics, Rice University, Houston, Texas USA

Stephen Quake, Department of Bioengineering, Stanford University, Palo Alto, California USA

Mark Ratner, Department of Chemistry, Northwestern University, Evanston, Illinois USA

David Reichman, Department of Chemistry, Columbia University, New York City, New~York USA

George Schatz, Department of Chemistry, Northwestern University, Evanston, Illinois USA

Steven J. Sibener, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois USA

Andrei Tokmakoff, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois USA

Donald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota USA

John C. Tully, Department of Chemistry, Yale University, New Haven, Connecticut, USA

PHYSICAL CHEMISTRY OF POLYELECTROLYTE SOLUTIONS

ADVANCES IN CHEMICAL PHYSICS

VOLUME 158

MITSURU NAGASAWA

Toyota Technological InstituteNagoya, Aichi-ken, Japan

Series Editors

STUART A. RICE

Department of ChemistryandThe James Franck InstituteThe University of ChicagoChicago, Illinois

AARON R. DINNER

Department of ChemistryandThe James Franck InstituteThe University of ChicagoChicago, Illinois

Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Nagasawa, Mitsuru, 1923-

Physical chemistry of polyelectrolyte solutions / Mitsuru Nagasawa.

pages cm. – (Advances in chemical physics ; volume 158)

Includes index.

ISBN 978-1-119-05708-6 (cloth)

1. Polyelectrolytes. 2. Electrolytes. 3. Electrolyte solutions. I. Title.

QD382.P64N34 2015

541′.372–dc23

2015019349

Preface to the Series

Advances in science often involve initial development of individual specialized fields of study within traditional disciplines followed by broadening and overlap, or even merging, of those specialized fields, leading to a blurring of the lines between traditional disciplines. The pace of that blurring has accelerated in the last few decades, and much of the important and exciting research carried out today seeks to synthesize elements from different fields of knowledge. Examples of such research areas include biophysics and studies of nanostructured materials. As the study of the forces that govern the structure and dynamics of molecular systems, chemical physics encompasses these and many other emerging research directions. Unfortunately, the flood of scientific literature has been accompanied by losses in the shared vocabulary and approaches of the traditional disciplines, and there is much pressure from scientific journals to be ever more concise in the descriptions of studies to the point that much valuable experience, if recorded at all, is hidden in supplements and dissipated with time. These trends in science and publishing make this series, Advances in Chemical Physics, a much needed resource.

The Advances in Chemical Physics is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

Stuart A. RiceAaron R. Dinner

Preface

Polyelectrolyte solutions are ubiquitous in nature; their properties define the behavior of important biological and physical processes, and many kinds of synthetic polyelectrolytes are utilized in our daily life and also in industry.