A study was carried out on the potentiometric titrations of poly(vinyl alcohol) partially acetalized with glyoxylic acid (PVAG). The titration curves were known to fulfil the relation proposed already by Pals and Hermans and the dissociation exponents were determined thereby. The radius of this polyacid was estimated from the electro-static free energy change by means of our theoretical treatment of polyelectrolyte solutions : it was found that the size decreased with the concentration, consistently with the well-known variation of the viscosity. Moreover, a potential potentiometrically obtained was shown not to be in agreement with the surface potential electrophoretically determined. This could be understood by referring the former to an average potential inside the spherical macro-ion

HOSONO, Masao

ISE, Norio

SAKURADA, Ichiro

English

Kyoto University Research Information Repository

RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:Potentiometric Titrations of aPolyelectrolyteSAKURADA, Ichiro; HOSONO, Masao; ISE, NorioSAKURADA, Ichiro ...[et al]. Potentiometric Titrations of a Polyelectrolyte. Memoirs of theFaculty of Engineering, Kyoto University 1958, 19(4): 402-4071958-02-01http://hdl.handle.net/2433/280397402 Potentiometric Titrations of a Polyelectrolyte By Ichiro SAKURADA, Masao HosoNo and Norio lsE Department of Textile Chemistry (Received July 17, 1957) Abstract A study was carried out on the potentiometric titrations of poly( vinyl alcohol) partially acetalized with glyoxylic acid (PV AG). The titration curves were known to fulfil the relation proposed already by Pals and Hermans and the dissociation exponents were determined thereby. The radius of this polyacid was estimated from the electro-static free energy change by means of our theoretical treatment of polyelectrolyte solutions: it was found that the size decreased with the concentration, consistently with the well-known variation of the viscosity. Moreover, a potential potentiometrically obtained was shown not to be in agreement with the surface potential electrophoretically determined. This could be understood by referring the former to an average potential inside the spherical macro-ion. Introduction A great deal of research has been accumulated on the potentiometric study of typical and weak polyelectrolytes. An empirical relation was established by Katchalsky1, 2 J to describe the titration curve. However, so much effort has not been devoted to the polyelectrolytes of larger dissociation constant as to those of small one. In an attempt to improve this situation, we have carried out the potentiometric study of poly( vinyl alcohol) partially acetalized with glyoxylic acid (PV AG). In this paper, confirming the validity of Pals-Hermann's relation on the titration, the size of macro-ion in non-extremely dilute solution and the radical discrepancy between electrophoretic and potentiometric potentials will be discussed from an unified theoretical stand-point. Titration Curve As is shown in Fig. 1, the titration curve of this polyacid differs clearly from that of weak polyacids in its shape, which is very close to that of strong normal acids. In order to obtain an empirical relation fitting this experimental result, it seems 5 ::r: 4 a... Potentiometric Titrations of a Polyelectrolyte 403 SAMPLE:S-C POLYMER CONCENTRATION (al 1.1 o 1 ( g✓1000cc) (b) 1.984 (C) 3.988 reasonable to introduce a correc-tion term due to self-dissociations of ionizable groups into Katchal-sky's relation. Calculation leads to the final expression a' = pK+n log1~-,, ( 1) -a l , 2L--_ _J.. _____ ..___ ___ _,_ __ __. 0 0.2 0.4 0.8 0.8 where a is the degree of neutrali-zation in its usual sense of word, pK the apparent dissociation ex-ponent, n a constant, [H+] the d,._ Fig. 1. Titration Curves of PVAG (I) concentration of hydrogen-ions, [CJ the total concentration of ionizable groups. a+[H+]/[C] corresponds to the ratio of the number of ionized groups to the total number of ionizable groups and it can be considered the extended degree of neutrali-zation. Eq. (1) has been already used by Pals and Hermann3 ) and, as is shown in Fig. 2, is found to fit our experimental data very closely. The values of pK evaluated are tabulated in Table 1. pK is practically constant over the concentration range covered by our experiment and shows a tendency to increase with the carboxyl group content, which can be interpreted reasonably in terms of the electrostatic interaction. Katchalsky observed =a SAMPLE: s-c POLYMER CONCENTRATION 5 4 x 1.10 l ( g/1000cc) o 1.984 • 3.968 2L------...l------7--------=~-~ -0.2 0 0.2 0.4 d.' 109 1-~' Fig. 2. Titration Curves of PVAG (II) 404 lchiro SAKURADA, Masao HoSONO and Norio ISE Table 1. Dissociation Exponents of PV AG ----I I Concentration Sample DP COOR-Content [ I pK (mo! %) (g./1000 cc.) I I 4.030 I 3.33 S-A 2150 12.08 2.015 3.33 0.918 3.33 I I I 2.916 I 2.60 S-7 1700 5.82 0.972 I 2.60 --· I I 6.940 I 2.55 S-8 1700 3.46 3.470 2.55 2.082 2.45 I 3.968 2.90 s-c 970 10.80 1.984 2.90 1.101 2.90 4.058 2.90 S-1 890 5.73 2.960 2.93 1.976 2.95 0.998 2.85 ' _., _______ 7.364 2.50 S-2 890 2.55 3.682 2.53 2.210 2.65 the concentration dependence of pK of polymethacrylic acid and showed that it dis-appeared when account was taken of the activity coefficient!). It seems most likely that such correction becomes necessary also for our case, upon going to higher carboxyl group contents and concentrations. Estimation of Molecular Size The ionized groups of polyelectrolytes are bound together on the polymer chain and are subjected to the interaction, much more stronger than that in the normal electrolyte solutions. The anomaly observed in its titration curve can be also attributed to this effect and measured by the electrostatic free energy F,. Generally, H K 1 a' 0.434 8F, p = p o+ og 1-a'+ kT az (2) holds, where pK0 denotes the dissociation exponent of the ionizable group in ideal state, k the Boltzmann constant, T the absolute temperature, Z the number of ionised groups of a macro-ion. On the other hand, the inter-macro-ion interaction has been brought to bear on the macroscopic behaviors of polyelectrolyte solutions by us, 4J on the bases of the model used by Hermans and Overbeek5 l and the interionic theory of Wicke and Eigen,6l and the thermodynamic quantities have been derived. In the case where the solution is salt-free and the number of gegen-ions fixed in the macro-ion is negligibly small compared to Z, and if mp' <f;._Z mp, it gives Potentiometric Titrations of a Polyelectrolvte 405 8Fe/8Z = -e\ Z,;;[2-r(,;;R) +a(,;;R)J-[_§_ _? _l] E 3 5 R 201 +; [-r(K01) +a(K01)], (3) where R is the radius of macro-ion, 01 the radii of ionized group and gegen-ion (assumed to be rigid spheres), e0 the electronic charge, K the extended Debye reciprocal radius K2 = 4Z?J.2 {Znp(Zmp+mp')}, mp= 1-np( ! -n:R 3), mp'=l-Znp({-noi"), np the average number of macro-ions per unit volume of solution, a(y)= !3 {1+y-1J_y-2ln(l+y)} and -r(y)= !3{ln(l+y)-y+~y2}. Combining Eq. (3) with the value of g~e obtained by Eq. (2) taking pK0 = 2.50, which is found by the graphical extrapolation of pK to zero carboxyl group content, the size of the marco-ion can be estimated. These values of R so obtained are tabulated in Table 2, with R', the extension of macro-ion viscometrically determined. The concentration dependence of R invites some interesting discussion. Table 2. Radii of PVAG from the Titration Data at a'=0.5 Sample I DP I COOR-Content I Concentration I R I R' (mo! %) (g./1000 cc.) (A) CA) 4 57 s-c 970 10.80 2 66 1 72 0 240 300 ! 4 52 S-1 890 5.73 2 60 1 67 I 0 170 290 --8 39 S-2 260 2.52 4 46 2 51 0 90 260 2R': The root mean square end-to-end distance of macro-ion determined by the intrinsic viscosity number by means of Flory-Fox Eq .. The well-known variation of "f/sPlc with concentration has been interpreted in terms of "intramolecular" interaction7l. However it seems to us unrealistic to take no account of the "intermolecular" interaction even in the dilute solutions of poly-electrolytes and the anomaly of viscosity can be attributed to this interaction, which becomes greater with concentration. We could say this alternative interpretation is supported by Table 2, judged from the very nature of our treatment. We are not in a position to quantitatively examine the magnitudes of R's in the non-extremely dilute solution : convincing information has not be obtained from other approaches. It can, however, be said that the decreasing tendency of R with concent-ration would be close to reality. 406 Ichiro SAKURADA, Masao HosoNo and Norio IsE Potentiometric and Electrophoretic Potentials The electrophoretic mobility m of a charged particle is related to the electro-phoretic potential ,,,, (surface potential) by m = K'ele" E_ T/ ( 4) where r; is the viscosity coefficient of the solvent, K a contant dependent on the size, shape and conductivity of the particle and so on. The potentiometric potential, which is defined by the relation ( 5) is described as the potential of field inside the macro-ion, from which H+-ion is brought to infinity. ,Pot may be equal to ,,1, only when the potential inside the macro-ion is i:cdependent of the distance from the centre. As illustrated in Table 3, however, the observed potentiometric potential, Oot obs, considerably differs from sele obs ,8l The discrepancy can be clearly understood if , Pot is to be refered to an average potential inside the spherical macro•-ion. According to our calculation,4l the potential inside the macro-ion ¢ 2 as a function of the distance r from the centre is given by ,,, = -Ze02 (,cR+3R 2 _ 2 ) 'fl 2 E R3 ,cR+ 1 r · (6) - 1 fR . Assuming ,Pot= c/Jz = R Jo c/J2dr, we obtam sPot/sele = (,cR+4)/3, (7) since ,,1,=Cc/J2)r-R, In Table 3, the observed electrophoretic potentials are compared with the observed potentiometric ones, and the validity of Eq. (7) undergoes an examination. Table 3. Comparison between Potentiometric and Electrophoretic Potentials Sample I C:ete obs X 105 (e.s.u.) I C:Pot cal X 105 (e.s.u.) C:Pot obs X 105 (e.s.u.) S-C 3.6 12 9.9 S-1 2.7 6.2 4.9 S-2 1.5 2.6 3.0 S-8 1.8 4.3 3.9 All values of ,,1, obs are obtained, from the extrapolated value of observed descending mobilites (at the concentration 4 g./1000 cc.) to zero ionic strength, by means of Eq. (4) with K=6~. Using the values of " at the concentration 4g./1000cc. and those of Rat this concentration shown in Table 2, ,pot cal is calculated from ,ele obs according Potentiometric Titrations of a Polyelectrolyte 407 to Eq. (4). (pot obs, which is evaluated by Eq. (5) from the observed values of ~~~ , is in a good agreement with ( pot cat, Experimental Preparation of PV AG. PV AG was prepared by acetalization of poly( vinyl alcohol) with glyoxylic acid. The details are found elsewhere9). The degree of poly-merization was determined by the viscosity measurement of parent PVA and the carboxyl group content was evaluated by the conductometric titration. Potentiometric titrations. The titrations were performed with a glass electrode at room temperature (about 25°C). The sensitivity of the potentiometer was 0.01 pH unit and the reproducibility of the data was 0.03 pH unit. Electrophoretic measurements. The electrophoresis was carried out by the moving-boundary method using the Tiselius apparatus. The details are given in another paper8J. References 1) A. Katchalsky and P. Spitnik: J. Polymer Sci., 2 432 (1947). 2) A. Katchalsky, N. Shavit and H. Eisenberg: J. Polymer Sci., 13 69 (1954). 3) D. Pals and J. Hermans: Ree. trav. chim., 71 513 (1952). 4) M. Hosono and N. Ise: in preparation. 5) J. Hermans and J Overbeek: Rec. trav. chim., 67 761 (1948). 6) E. Wicke and M. Eigen: Z. Elektrochem., 56 551 (1952). 7) R. M. Fuoss: Dis. Faraday Soc., 11 125 (1952). 8) N. Ise, M. Hosono and I. Sakurada: Chem. High Polymers, Japan, in press. 9) A. Nakajima, S. Ishida and I. Sakurada: Chem. High Polymers, Japan, 14 259 1957. 

Potentiometric Titrations of a Polyelectrolyte

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Potentiometric Titrations of a Polyelectrolyte

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