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Gel permeation chromatography of flexible polymers on macroporous, swollen absorbents
Gel permeation chromatography of flexible polymers
833
relationship explains the fact that the dependence on reaction temperature of the molecular weight of polyarylates prepared by accepter catalysed polyesterification contains a number of maxima and minima. Translated by E. O. PHILLI~S REFERENCES 1. S. V. VINOGRADOVA, V. V. VASNEV, V. V. KORSHAK, T. I. MITAISHVILI and A. V. VASILEV, Dokl. Akad. Nauk SSSR 187: 1297, 1969 2. V. V. TURSKA, E. TURSKA, A. V. VASILEV, M. SINYARSKA-KAPUSTINSKA, S. V. VINOGRADOVA and V. A. VASNEV, Vysokomol. soyed. A14: 1267, 1972 (Translated in Polymer Sei. U.S.S.R. 14: 6, 1417, 1972) 3. V. V. KORSHAK, S. V. VINOGRADOVA, V. A. VASNEV and T. I. MITAISHVILI, Vysokomol. soyed. A l h 81, 1969 (Translated in Polymer Sci. U.S.S.R. 11: 1, 89, 1969 4. V. V. KORSHAK, V. A. VASNEV, S. V. BOGATKOV, A. I. TARASOV and S. V. VINOGRADOVA, Reakts. sposob, organ, soyed. 1O: 375, 1973 5. S. V. BOGATKOV and Ye. M. CHERKASOVA, Zh. obsheh, khim. 39: 1861, 1969 6. K. KIMURA and R. FUJISHIRO, Bull. Chem. Soc. J a p a n 31: 435, 1958 7. F. CRUEGE, P. PINEAU and J. LASCOMBE, J. chim. phys. et phys.-cAirn, biol. 64: 1161, 1967 8. A. A. MASHKOVSKII and S. Ye. ODINOKOV, Dokl. Akad. Nauk SSSR 204: 1165, 1972 9. H. BABA, A. MATSUYAMA and H. KOKUBIN, J. Chem. Phys. 41: 895, 1964 10. S. BENSON, Termokhimicheskaya kinetika (Thermomechanical Kinetics). Izd. "Mir", 1971 (Russian translation)
GEL PERMEATION CHROMATOGRAPHY OF FLEXIBLE POLYMERS ON MACROPOROUS, SWOLLEN ABSORBENTS* L. Z.
VILENCHIK, B. G. BELEN'KII, V. V.
NESTEROV,
V. I. KOLEGOV a n d
S. YA. FRENK~L' I n s t i t u t e of Macromolecular Compounds, U.S.S.R. Academy of Sciences
(Received 27 July 1973) I t is shown that in chromatography of flexible chain polymers on macroporous, swollen absorbents the components are separated in the main by two mechanisms, namely the molecular sieve and occlusion mechanisms. The latter is dependent on the thermodynamic compatibility of the polymer molecules with the absorbent matrix. Macromolecules t h a t are incompatible with the absorbent are completely excluded from the compact regions of the latter, while compatible macromolecules are able to penetrate into these regions, which affects the retention volume and results in deviation from Benoit's principle of universal calibration. The exclusion effect can be described by analogy with the exclusion volume of polymer molecules a n d thus enables information to be obtained about the constants of interaction of polymer segments with one another, with the absorbent a n d with the solvent, by the use of gel permeation chromatography. * Vysokomol. soyed, h17: No. 4, 726-730, 1975.
834
L . Z . ViT,~.~cm~ et al.
S~P~ATIO~ of macromoleeular components by gel permeation chromatography (GPC) is brought about by several mechanisms. Of these the main ones are the molecular sieve [1-4], the diffusion [5-9] and the exclusion (i.e. the mechanism of volume exclusion) [10-12] mechanisms. The overall effect of these mechanisms is more rapid movement of the larger molecules along the chromatographic column, in comparison with the movement of the macromolecules of smaller size. The principle of the molecular sieve mechanism depends on the macromolecules being eluted and the pores of the absorbent, being of similar size. The diffusion mechanism is dependent on the mobility of the polymer molecules in the stationary phase of the column. The extent to which it is a non-equilibrium process is dependent on this. The basis of the exclusion mechanism is the effect of the exclusion volume of the polymer segments, which is typical of macromolecules [13]. Usually an effort is made to carry out GPC experiments under conditions close to equilibrium conditions. Then the effect of the diffusion mechanism on the separation of nmcromolecules becomes of little importance. When however unswoUen absorbents such as sintered glasses, silica gels or styrogels are used as packings, where the volume effect in interaction between the macromolecules and the matrix of the absorbent does not, in principle, arise, the molecular sieve effect alone comes into play in the GPC process. Then in interpretation of the chromatograms Benoit's principle of universal calibration [14, 15] applies satisfactorily to the MVCD of the polymers. According to this principle GPC separation of macromoleeules occurs according to their hydrodynamic volumes V ~ M [7]This principle is also widely used in GPC on swollen absorbents (gels), which is far from being correct in all instances. We have recently reported a substantial deviation from universal calibration in gel permeation chromatography on Sephadex's [16]. Gel chromatography of three types of polymer, namely dextrans, polyvinylpyrrolidone (PV'P) and poly(ethylene glycols) (PEG), was carried out in columns of length 96 cm a n d internal diameter 20 nun, packed with Sephadex G-75 and Sephadex G-100 (particle diameter 60-120 ~). The flow rate of the eluent (0.3% aqueous NaC1 solution) was 50 ml/hr. A differential in-line refraetometer with a cell volume of 50/~1 and a sensitivity of ztn=10 -s was used as the detector.
The results are presented in Fig. 1. It is seen that the dependence of the retention volume V on log (M[~]) differs markedly on the one hand for P V P and the dextrans, and for PEG on the other. Moreover the logarithm of the difference hi the values of lz is inversely proportional to the molecular weight of the PVP or dextran (Fig. 2). These results can be explained in the following way. I n GPC on swollen absorbents the macromoleeules, by the molecular sieve mechanism, penetrate into the macro-pores of the absorbent with different probabilities, depending on their hydrodynamic dimensions. The volume of absorbent accessible to the macromoleeules (Va) is dependent on the sum of the volumes of these pores, and consequently so is the retention volume V. This relationship is universal, i.e. it is common to all types of maeromoleeule. The walls o f the macro-pores of swollen absorbents are however permeable to polymer chain
Gel permeation chromatography of flexible polymers
835
units, and with a certain probability these can penetrate the walls into dense regions of the absorbent, i.e. into micro-pores, thus increasing the accessible volume of the absorbent by some quantity A Vs. This ability of polymer Io! (MkJ)
(M[¢]) a
h
~
3 I
100
I
150
I 2
Ioo
200
15o
t2
200
l
v,m/
250
FIG. 1. Dependence of the retention volmne on the logarithm of the product of the molecular weight and intrinsic viscosity of the polymer, in columns packed with Sephadex G-100 (a) and G-75 (b). a: 1--Dextran, 2--PVP, 3 - - P E G ; b: / - - P E G , 2--dextran, 3--theoretical curves for dextran obtained by means of equation (6) at Z*~0.47.
chain molecules to diffuse into the dense regions of a swollen absorbent is closely related to the thermodynamic compatibility of the macromolecules being subjected to chromatographic separation with the matrix of the absorbent, and can be interpreted within the framework of the excluded volume concept [13] as a characteristic additional to the molecular sieve factor. For polymer molecules compatible with a given absorbent AVa can be calculated in the following way. We shall regard the absorbent swollen in a solvent (gel) as a solution of macromolecules, the role of which is fulfilled by the dense regions of each gel particle. The free energy of mixing of the polymer and solvent can be calculated for such a solution by the standard method [17]. Then the change in free energy caused by penetration into dense regions of the gel, of segments of the macromolecules being eluted, can be determined easily by making use of the analogy with the excluded volume of polymer molecules [13]. Representing each dense region of gel as a sphere of radius R, uniformly filled with chain units, which is much larger than the macromolecule and is regarded as a gaussian coil (R>>(~)J, where (~2)t is the radius of inertia of the macromolecule) the expression for the total change in free energy of the gel macromolecule-solvent system when a macromoleeule approaches a dense region up to a distance a, calculated for one macromolecule, can by analogy with reference [17] be written in the form
ziFa=kT---~l
(k-l)! I PgpmdV~-,~=2 ~inlg~_i~n) (V~-iV~m--~)X
x ~ PgPm . ~+i-~d V - - ( X l g + X l m )
i
Vl i Pmp~V] Pmpg~V+,~graTr rg .]
(1)
836
L.Z. V~cmK
et
al.
Here V1 is the volume of the solvent molecule, Vg and Vm the volumes o f the units of the gel and macromolecule, pg and pm the number of units of gel and macromoleeule per unit volume, a the distance between the centre of the dense region of gel and the centre of the macromolecule, Xlg and Xlm the constants of interaction of units of gel and the macromolecule with the solvent, and Xgm the constant characterizing interaction between the gel and the macromolecule in the given solvent. Within the dense regions pg approaches zero. Carrying out the integration in equation (1), and for simplicity neglecting the series in it (becasue of its low value) we obtain 0, when a > / ~
ZFa=llcTI, ~WgVm[ l=Xgm -#-g wl --(Xlg-}-Zlm)IPgZ'
when
aHR
(2)
Here Z=M/Mo is the number of units in the macromolecule and M0 is the weight of a unit. The change in the free ~nergy AFa corresponds to the probability exp [--AS'a/ kT] that the macromolecule will be at a distance a from a dense region of gel. The product exp [--AFa/kT]4rtaSda thus represents the part of a spherical layer of gel that is accessible to the macromolecule. Extending the integration with respect to a over the entire gel particle and allowing for the fraction of dense regions in each particle, we find a Va=
Vg-- Va. ~.' o ~-.- j 4na ° exp [--AF Vg
(a)/kT]da
(3}
0
Here Rg is the radius of a swollen gel particle, Vg its total volume and Va the volume of gel accessible to the macromolecules by the molecular sieve mechanism. I f under the conditions of a given GPC experiment the polymer molecules being eluted are incompatible with the gel network the retention volume Vile will be determined entirely by Va,
v ~ = Vo+ v,,.
(4)
For a polymer that is compatible with the gel we have another relationship
Vo= Vo+ Va.+ zf Va= Vi/~+ A Va
(5)
where A Va is defined by equation (3) and V0 is the volume of the channels o f the mobile phase in the given chromatographic system. Equations (2)-(5) show that if the values of the Flory-Huggins constants Xlm, Zig and Xgm are available, and knowing the retention volumes for polymers known to be incompatible with the absorbent under given conditions, it is easy to calculate the retention volumes for compatible polymers. Conversely the constants X1j can be found from the values of Ve and Viie. In our experiments P E G was incompatible with the absorbent and PVP and dextran were compatible with it. The choice of a dextran gel, i.e. Sephadex, as the absorbent enabled
Gel permeation chromatography of flexible polymers
837
us to put X1g=Xlm--X* and X ~ n : 0 in calculation of AVa. The calculation was made by means of the formula Vc= Vttc-~( ~k-- Vl/¢) exp [--kcMo)
(6)
which is obtained from (5) by substituting for 3 Va its value from (3). In equation (6) Vk is the total volume of the chromatographic system, M c the molecular weight of the dextran and k¢ a parameter characterizing the system Sephadex1 AFa dextran-aqueous NaC1 solution, given by ko-- Me kT t a
MoV1
x*= (1-ko VVmpd
(7)
The retention volumes obtained in experiments in a column packed with Sephadex G-100 were substituted in formula (6). The parameter kc was found and then the constant X* was calculated from formula (7). The results of the calculations are presented below Mol. weight of dextran X* from equation (7)
5 × 10a 7 × 10~ 1 x 104 5 × 104 0.45 0.48 0-47 0.49
Z/v=0.4~ The average value of the Flory-Huggins constant found in this way for dextran ( f l y = 0.47) was used for calculation of the retention volume for dextran eluted through a column of Sephadex G-75, which differs from Sephadex G-1O0 5 •
2
30
I'0.I0"*
2.0.I0-*
M
lq'Io. 2. Logarithm of the difference between the retention volumes for PEG and dextran
as a function of the molecular weight of the dextran, in columns packed with Sephadox G-100 (1) and G-75 (2). in density, porosity and degree of swelling. Here, as in the previous instance, the retention voIumcs of polymers incompatible with Sephadex were t a k e n as being the same as the retention volumes for poly(ethylene glycol). The results of the calculations are presented in Fig. lb. The experimental results lie within 15% of the calculated values.
838
B. L LIROVA. e$ al.
These results, in combination with the dependence of In (A Va) on the molecular weight of dextran, depicted in Fig. 2, which is in agreement with equa~ tion (6) predicated by theory, give an indication of the adequacy of our proposed model of gel permeation chromatography of flexible chain polyfi~ers on swollen absorbents. The authors are grateful to Yu. Ye. Eizner and Yu. Ya. Gotlib for fruitful discussion of problems encountered in the work. Translated by E. O. P~LI~PS REFERENCES 1. 2. 3. 4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17.
J. PORATH, Pure Appl. Chem. 6: 233, 1963 T. LOURENT and J. KILLANDER, J. Chromatogr. 14: 317, 1964 P. SQUIRE, Anal. Biochem. Biophys. 107: 471, 1964 A. DEVRIES, IUPAC International Symposium on Macromolecular Chemistry, Prague, 1965 G. ACKERS, Biochemistry 3: 723, 1964 W. YAU and C. MALONE, J. Polymer Sei. B5: 663, 1967 W. YAU. H. SUCHAN and J. MALONE, J. Polymer Sci. A-2, 6: 1349, 1968 W. YAU, C. MALONE and S. FLEMING, J. Polymer Sci. B6: 803, 1968 T. GERMANS, J. ,Polymer Sci. A-2, 6: 1217, 1968 C. LATHER and C. RUTHVEN, Biochem J. 62: 665, 1956 K. PEDERSON, Arch. Biochem. Biophys. 1: 157, 1962 P. FLODIN, J. Chromatogr. 5: 103, 1961 P. J. FLORY, Principles of Polymer Chemistry, New York, 1953 H. BENOIT, Z. GRUBISIC, P. REMPP, D. DECKER and J. ZILLIOX, J. Chem. Phys. 63: 1507, 1966 Z. GRUBISIC, P. REMPP and H. BENOIT, J. Polymer Sci. B5: 753, 1967 B. G. BELEN'KII, L. Z. VILENCHIK, V. V. NESTEROV and T. I. SHASH:INA, Vysokomol, soyed: AI5: 2614, 1973 (Translated in Polymer Sci. U.S.S.R. 15: 11, 2973, 1973) V. N. TSVETKOV, V. Ye. ESKIN and S. Ya. FRENKEL', Struktura makromolekul v rastvorakh (Structure of Macromolecules in Solution). Izd. "Nauka", 1964
SPECTROSCOPIC INVESTIGATION OF IOI~-MOLECULE INTERACTIONS IN POLYMER SOLUTIONS* B. I. Lmovx, A. L. SMOLYANSKII,A. A. TAGER and V. S. BLINOV A. IV[. Gor'kii Urals State University Vologod Dairy Institute
(Received 25 October 1973) The interaction between a number of inorganic salts and polyvinyl acetate (PVAc), a vinyl alcohol-vinyl acetate copolymer (VA-VAc) and polyvinyl alcohol (PVA) has been studied. I t has been shown that, when perchlorates are introduced * Vysokomol, soyed. A17: Do. 4, 731-737, 1975.
833
relationship explains the fact that the dependence on reaction temperature of the molecular weight of polyarylates prepared by accepter catalysed polyesterification contains a number of maxima and minima. Translated by E. O. PHILLI~S REFERENCES 1. S. V. VINOGRADOVA, V. V. VASNEV, V. V. KORSHAK, T. I. MITAISHVILI and A. V. VASILEV, Dokl. Akad. Nauk SSSR 187: 1297, 1969 2. V. V. TURSKA, E. TURSKA, A. V. VASILEV, M. SINYARSKA-KAPUSTINSKA, S. V. VINOGRADOVA and V. A. VASNEV, Vysokomol. soyed. A14: 1267, 1972 (Translated in Polymer Sei. U.S.S.R. 14: 6, 1417, 1972) 3. V. V. KORSHAK, S. V. VINOGRADOVA, V. A. VASNEV and T. I. MITAISHVILI, Vysokomol. soyed. A l h 81, 1969 (Translated in Polymer Sci. U.S.S.R. 11: 1, 89, 1969 4. V. V. KORSHAK, V. A. VASNEV, S. V. BOGATKOV, A. I. TARASOV and S. V. VINOGRADOVA, Reakts. sposob, organ, soyed. 1O: 375, 1973 5. S. V. BOGATKOV and Ye. M. CHERKASOVA, Zh. obsheh, khim. 39: 1861, 1969 6. K. KIMURA and R. FUJISHIRO, Bull. Chem. Soc. J a p a n 31: 435, 1958 7. F. CRUEGE, P. PINEAU and J. LASCOMBE, J. chim. phys. et phys.-cAirn, biol. 64: 1161, 1967 8. A. A. MASHKOVSKII and S. Ye. ODINOKOV, Dokl. Akad. Nauk SSSR 204: 1165, 1972 9. H. BABA, A. MATSUYAMA and H. KOKUBIN, J. Chem. Phys. 41: 895, 1964 10. S. BENSON, Termokhimicheskaya kinetika (Thermomechanical Kinetics). Izd. "Mir", 1971 (Russian translation)
GEL PERMEATION CHROMATOGRAPHY OF FLEXIBLE POLYMERS ON MACROPOROUS, SWOLLEN ABSORBENTS* L. Z.
VILENCHIK, B. G. BELEN'KII, V. V.
NESTEROV,
V. I. KOLEGOV a n d
S. YA. FRENK~L' I n s t i t u t e of Macromolecular Compounds, U.S.S.R. Academy of Sciences
(Received 27 July 1973) I t is shown that in chromatography of flexible chain polymers on macroporous, swollen absorbents the components are separated in the main by two mechanisms, namely the molecular sieve and occlusion mechanisms. The latter is dependent on the thermodynamic compatibility of the polymer molecules with the absorbent matrix. Macromolecules t h a t are incompatible with the absorbent are completely excluded from the compact regions of the latter, while compatible macromolecules are able to penetrate into these regions, which affects the retention volume and results in deviation from Benoit's principle of universal calibration. The exclusion effect can be described by analogy with the exclusion volume of polymer molecules a n d thus enables information to be obtained about the constants of interaction of polymer segments with one another, with the absorbent a n d with the solvent, by the use of gel permeation chromatography. * Vysokomol. soyed, h17: No. 4, 726-730, 1975.
834
L . Z . ViT,~.~cm~ et al.
S~P~ATIO~ of macromoleeular components by gel permeation chromatography (GPC) is brought about by several mechanisms. Of these the main ones are the molecular sieve [1-4], the diffusion [5-9] and the exclusion (i.e. the mechanism of volume exclusion) [10-12] mechanisms. The overall effect of these mechanisms is more rapid movement of the larger molecules along the chromatographic column, in comparison with the movement of the macromolecules of smaller size. The principle of the molecular sieve mechanism depends on the macromolecules being eluted and the pores of the absorbent, being of similar size. The diffusion mechanism is dependent on the mobility of the polymer molecules in the stationary phase of the column. The extent to which it is a non-equilibrium process is dependent on this. The basis of the exclusion mechanism is the effect of the exclusion volume of the polymer segments, which is typical of macromolecules [13]. Usually an effort is made to carry out GPC experiments under conditions close to equilibrium conditions. Then the effect of the diffusion mechanism on the separation of nmcromolecules becomes of little importance. When however unswoUen absorbents such as sintered glasses, silica gels or styrogels are used as packings, where the volume effect in interaction between the macromolecules and the matrix of the absorbent does not, in principle, arise, the molecular sieve effect alone comes into play in the GPC process. Then in interpretation of the chromatograms Benoit's principle of universal calibration [14, 15] applies satisfactorily to the MVCD of the polymers. According to this principle GPC separation of macromoleeules occurs according to their hydrodynamic volumes V ~ M [7]This principle is also widely used in GPC on swollen absorbents (gels), which is far from being correct in all instances. We have recently reported a substantial deviation from universal calibration in gel permeation chromatography on Sephadex's [16]. Gel chromatography of three types of polymer, namely dextrans, polyvinylpyrrolidone (PV'P) and poly(ethylene glycols) (PEG), was carried out in columns of length 96 cm a n d internal diameter 20 nun, packed with Sephadex G-75 and Sephadex G-100 (particle diameter 60-120 ~). The flow rate of the eluent (0.3% aqueous NaC1 solution) was 50 ml/hr. A differential in-line refraetometer with a cell volume of 50/~1 and a sensitivity of ztn=10 -s was used as the detector.
The results are presented in Fig. 1. It is seen that the dependence of the retention volume V on log (M[~]) differs markedly on the one hand for P V P and the dextrans, and for PEG on the other. Moreover the logarithm of the difference hi the values of lz is inversely proportional to the molecular weight of the PVP or dextran (Fig. 2). These results can be explained in the following way. I n GPC on swollen absorbents the macromoleeules, by the molecular sieve mechanism, penetrate into the macro-pores of the absorbent with different probabilities, depending on their hydrodynamic dimensions. The volume of absorbent accessible to the macromoleeules (Va) is dependent on the sum of the volumes of these pores, and consequently so is the retention volume V. This relationship is universal, i.e. it is common to all types of maeromoleeule. The walls o f the macro-pores of swollen absorbents are however permeable to polymer chain
Gel permeation chromatography of flexible polymers
835
units, and with a certain probability these can penetrate the walls into dense regions of the absorbent, i.e. into micro-pores, thus increasing the accessible volume of the absorbent by some quantity A Vs. This ability of polymer Io! (MkJ)
(M[¢]) a
h
~
3 I
100
I
150
I 2
Ioo
200
15o
t2
200
l
v,m/
250
FIG. 1. Dependence of the retention volmne on the logarithm of the product of the molecular weight and intrinsic viscosity of the polymer, in columns packed with Sephadex G-100 (a) and G-75 (b). a: 1--Dextran, 2--PVP, 3 - - P E G ; b: / - - P E G , 2--dextran, 3--theoretical curves for dextran obtained by means of equation (6) at Z*~0.47.
chain molecules to diffuse into the dense regions of a swollen absorbent is closely related to the thermodynamic compatibility of the macromolecules being subjected to chromatographic separation with the matrix of the absorbent, and can be interpreted within the framework of the excluded volume concept [13] as a characteristic additional to the molecular sieve factor. For polymer molecules compatible with a given absorbent AVa can be calculated in the following way. We shall regard the absorbent swollen in a solvent (gel) as a solution of macromolecules, the role of which is fulfilled by the dense regions of each gel particle. The free energy of mixing of the polymer and solvent can be calculated for such a solution by the standard method [17]. Then the change in free energy caused by penetration into dense regions of the gel, of segments of the macromolecules being eluted, can be determined easily by making use of the analogy with the excluded volume of polymer molecules [13]. Representing each dense region of gel as a sphere of radius R, uniformly filled with chain units, which is much larger than the macromolecule and is regarded as a gaussian coil (R>>(~)J, where (~2)t is the radius of inertia of the macromolecule) the expression for the total change in free energy of the gel macromolecule-solvent system when a macromoleeule approaches a dense region up to a distance a, calculated for one macromolecule, can by analogy with reference [17] be written in the form
ziFa=kT---~l
(k-l)! I PgpmdV~-,~=2 ~inlg~_i~n) (V~-iV~m--~)X
x ~ PgPm . ~+i-~d V - - ( X l g + X l m )
i
Vl i Pmp~V] Pmpg~V+,~graTr rg .]
(1)
836
L.Z. V~cmK
et
al.
Here V1 is the volume of the solvent molecule, Vg and Vm the volumes o f the units of the gel and macromolecule, pg and pm the number of units of gel and macromoleeule per unit volume, a the distance between the centre of the dense region of gel and the centre of the macromolecule, Xlg and Xlm the constants of interaction of units of gel and the macromolecule with the solvent, and Xgm the constant characterizing interaction between the gel and the macromolecule in the given solvent. Within the dense regions pg approaches zero. Carrying out the integration in equation (1), and for simplicity neglecting the series in it (becasue of its low value) we obtain 0, when a > / ~
ZFa=llcTI, ~WgVm[ l=Xgm -#-g wl --(Xlg-}-Zlm)IPgZ'
when
aHR
(2)
Here Z=M/Mo is the number of units in the macromolecule and M0 is the weight of a unit. The change in the free ~nergy AFa corresponds to the probability exp [--AS'a/ kT] that the macromolecule will be at a distance a from a dense region of gel. The product exp [--AFa/kT]4rtaSda thus represents the part of a spherical layer of gel that is accessible to the macromolecule. Extending the integration with respect to a over the entire gel particle and allowing for the fraction of dense regions in each particle, we find a Va=
Vg-- Va. ~.' o ~-.- j 4na ° exp [--AF Vg
(a)/kT]da
(3}
0
Here Rg is the radius of a swollen gel particle, Vg its total volume and Va the volume of gel accessible to the macromolecules by the molecular sieve mechanism. I f under the conditions of a given GPC experiment the polymer molecules being eluted are incompatible with the gel network the retention volume Vile will be determined entirely by Va,
v ~ = Vo+ v,,.
(4)
For a polymer that is compatible with the gel we have another relationship
Vo= Vo+ Va.+ zf Va= Vi/~+ A Va
(5)
where A Va is defined by equation (3) and V0 is the volume of the channels o f the mobile phase in the given chromatographic system. Equations (2)-(5) show that if the values of the Flory-Huggins constants Xlm, Zig and Xgm are available, and knowing the retention volumes for polymers known to be incompatible with the absorbent under given conditions, it is easy to calculate the retention volumes for compatible polymers. Conversely the constants X1j can be found from the values of Ve and Viie. In our experiments P E G was incompatible with the absorbent and PVP and dextran were compatible with it. The choice of a dextran gel, i.e. Sephadex, as the absorbent enabled
Gel permeation chromatography of flexible polymers
837
us to put X1g=Xlm--X* and X ~ n : 0 in calculation of AVa. The calculation was made by means of the formula Vc= Vttc-~( ~k-- Vl/¢) exp [--kcMo)
(6)
which is obtained from (5) by substituting for 3 Va its value from (3). In equation (6) Vk is the total volume of the chromatographic system, M c the molecular weight of the dextran and k¢ a parameter characterizing the system Sephadex1 AFa dextran-aqueous NaC1 solution, given by ko-- Me kT t a
MoV1
x*= (1-ko VVmpd
(7)
The retention volumes obtained in experiments in a column packed with Sephadex G-100 were substituted in formula (6). The parameter kc was found and then the constant X* was calculated from formula (7). The results of the calculations are presented below Mol. weight of dextran X* from equation (7)
5 × 10a 7 × 10~ 1 x 104 5 × 104 0.45 0.48 0-47 0.49
Z/v=0.4~ The average value of the Flory-Huggins constant found in this way for dextran ( f l y = 0.47) was used for calculation of the retention volume for dextran eluted through a column of Sephadex G-75, which differs from Sephadex G-1O0 5 •
2
30
I'0.I0"*
2.0.I0-*
M
lq'Io. 2. Logarithm of the difference between the retention volumes for PEG and dextran
as a function of the molecular weight of the dextran, in columns packed with Sephadox G-100 (1) and G-75 (2). in density, porosity and degree of swelling. Here, as in the previous instance, the retention voIumcs of polymers incompatible with Sephadex were t a k e n as being the same as the retention volumes for poly(ethylene glycol). The results of the calculations are presented in Fig. lb. The experimental results lie within 15% of the calculated values.
838
B. L LIROVA. e$ al.
These results, in combination with the dependence of In (A Va) on the molecular weight of dextran, depicted in Fig. 2, which is in agreement with equa~ tion (6) predicated by theory, give an indication of the adequacy of our proposed model of gel permeation chromatography of flexible chain polyfi~ers on swollen absorbents. The authors are grateful to Yu. Ye. Eizner and Yu. Ya. Gotlib for fruitful discussion of problems encountered in the work. Translated by E. O. P~LI~PS REFERENCES 1. 2. 3. 4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17.
J. PORATH, Pure Appl. Chem. 6: 233, 1963 T. LOURENT and J. KILLANDER, J. Chromatogr. 14: 317, 1964 P. SQUIRE, Anal. Biochem. Biophys. 107: 471, 1964 A. DEVRIES, IUPAC International Symposium on Macromolecular Chemistry, Prague, 1965 G. ACKERS, Biochemistry 3: 723, 1964 W. YAU and C. MALONE, J. Polymer Sei. B5: 663, 1967 W. YAU. H. SUCHAN and J. MALONE, J. Polymer Sci. A-2, 6: 1349, 1968 W. YAU, C. MALONE and S. FLEMING, J. Polymer Sci. B6: 803, 1968 T. GERMANS, J. ,Polymer Sci. A-2, 6: 1217, 1968 C. LATHER and C. RUTHVEN, Biochem J. 62: 665, 1956 K. PEDERSON, Arch. Biochem. Biophys. 1: 157, 1962 P. FLODIN, J. Chromatogr. 5: 103, 1961 P. J. FLORY, Principles of Polymer Chemistry, New York, 1953 H. BENOIT, Z. GRUBISIC, P. REMPP, D. DECKER and J. ZILLIOX, J. Chem. Phys. 63: 1507, 1966 Z. GRUBISIC, P. REMPP and H. BENOIT, J. Polymer Sci. B5: 753, 1967 B. G. BELEN'KII, L. Z. VILENCHIK, V. V. NESTEROV and T. I. SHASH:INA, Vysokomol, soyed: AI5: 2614, 1973 (Translated in Polymer Sci. U.S.S.R. 15: 11, 2973, 1973) V. N. TSVETKOV, V. Ye. ESKIN and S. Ya. FRENKEL', Struktura makromolekul v rastvorakh (Structure of Macromolecules in Solution). Izd. "Nauka", 1964
SPECTROSCOPIC INVESTIGATION OF IOI~-MOLECULE INTERACTIONS IN POLYMER SOLUTIONS* B. I. Lmovx, A. L. SMOLYANSKII,A. A. TAGER and V. S. BLINOV A. IV[. Gor'kii Urals State University Vologod Dairy Institute
(Received 25 October 1973) The interaction between a number of inorganic salts and polyvinyl acetate (PVAc), a vinyl alcohol-vinyl acetate copolymer (VA-VAc) and polyvinyl alcohol (PVA) has been studied. I t has been shown that, when perchlorates are introduced * Vysokomol, soyed. A17: Do. 4, 731-737, 1975.