Methods of investigations temperature precipitation as a method for polymer fractionation

METHODS OF INVESTIGATION TEMPERATURE PRECIPITATION AS A METHOD FOR POLYMER FRACTIONATION* V. M. GOL'DBERG, I. M. BEL'GOVSKII a n d A. L. IZYUlVIlVlKOV Institute of Chemical Physics, U.S.S.R. Academy of Sciences

(Received 12 November 1969) THE MOLECULAR weight distribution (MWD) of polymers not only provides information about the reaction mechanism of polymerization and degradation, but is also directly related to the technological properties of the polymer. I t is assumed that low molecular weight polymer fractions are special plasticizers, whereas molecules of high molecular weight ensure the strength of the pol3~mer material [1]. Fractioimtioix by temperature precipitation of polymer from solution is one of the various methods of determining the MWD of polymers [2]. The main feature of the method is the stepwise separation of fractions forming the polymer on reducing the temperature of the dilute solution1. Fractions are separated as a consequer~ce of the dependence of macromolecular solubility on molecular weight. Methodologically fractionation by temperature precipitation is similar to cor~ve~xtional turbidimetric titration [3]; however, it has several significant advantages over this method [4]. For example, the constancy of the volume of the solutio,~ examined and its optical properties simplify mlalysis of results: the abselme of large volumes, the temperature of which is thermostatically controlled, makes it co~vexfient from a techlxic~l point of view to use polymers which only dissolve at high temperatures; the possibility of repeated reproduction of experime,xts and of comparillg results of heating aild cooling. Apart from the advantages of temperature precipitation, the chief of which is the speed of obtainh~g information about polydispersion ( ~ 2 hr) and the possibility of using small amounts of polymer (a few milligrams), all the shortcomings of other methods of polymer fractionation, based oi~ difference in solubility of fractions, are ir~herez~t in this method. The dependence of solubility not oIfly or~ molecular weight, but also on polymer chain structure (branching), polymer crystallinity and other factors makes it difficult to obtain correct results and hflxders analysis a~d interpretation. From ai~ experimelltal poh~t of view the method of temperature preeipitatioI~ is fairly simple, nevertheless correct, results of MWD measurement can only be obtait~ed when certain occasionally very stringerlt requiremelxts are observed i~x relation to the couditiorls of polymer precipitation from solutions. Some problems involved in experimental methods, due to the selection of solvent, precipitant, polymer and stabilizer concel~tration, which are general for methods of temperature p~ecipitatiou and turbidimetric titratio~x, have been discussed repeatedly in the literature [3, 5, 6]. I n this study we will only deal with two problems related to important details of temperature precipitation: the possibility, in principle, of replacing the measurement of solution turbidity by the measureme~lt of light scattering inteIxsity at a certain angle * Vysokomol. soyed. A13: No. 4, 977-981, 1971. 1102

T e m p e r a t u r e precipitation as a ln(,thod fi~r l)olym('r fractionation .f observation tion..

altd

the

calculation

of o p t i m u m

t,emperatur(,

1 103

con(titi(ms of fl'acthma-

R e l a t i o n betwee~ t u r b i d i t y a n d light s c a t t e r i n g i n t e n s i t y at a c e r t a i , a m fie of observatioJ~.

l.lt the i~fitial stages of d e v e l o p i n g the m e t h o d of t e m p e r a t u r e precipitatiott ~tm g r a v i m e t r i c proportiolt of p o l y m e r p r e c i p i t a t e d from solution was e s t i m a t e d from t u r b i d i t y measurere(rots. A c c o r d i n g to the L a m b e r t - B e e r law, the absorptio~t coefficient ()f a uolnti(Ht (h') is siml)ly related to, and flmctions as a measure of, the eonc~mtT'a, tiolt of the absori)mg agent c. K =Kc

(1)

where, K is the Beer cotmtant. F r o m a practical p o i n t of view light absorpti(m during pr(,cil)itaiiojt ()t' ~ c(~lourless p o l y m e r f r o m a highly diluted soluti(m only slightly depends (m the scattering mechanism. bt this ease the a b s o r p t i o n coefficient K is identical w i t h r - - t h e t u r b i d i t y of the s.luti(m and c m m o t be m e a s u r e d w i t h sufficient a c c u r a c y ~s a sligltt differtmce between tw() large values by the w e a k e n i n g of intensity of the light b e a m going thr(mgh the cell. Accordittg to a well-known formula bt Epass = I n ( l - - ~ ' s ~ Eo

(2)

E , ] -- -- rA:c,

where E0 is the energy of inci(tent light, flow; E,)ass is the tlow energy passi)~g t h r o u g h the solution; E~c is the flow e~mrgy se'(ttered by the solut ion; A,c is the thicklmsS ()f the start ering solutiolt layer. H o w e v e r , in this ease the solutioa t u r b i d i t y is fairl 5 a c c u r a t e l y d e t e r m i n e d by the overall onergy of scattering. Thus, expmtsion m series of expressi(m (2) by E ~ , / E . gives r--

l E.,~ -. Ax E,

(3)

[f the distributiort f u n c t i o n of scatterfi~g particles according to (tmw~tsiolts ix in(lcpolMe~tt (~[' their co~),eentratioi~ m soluti(m, i.e. remains Ulu~'ha~),ged (Im'ilLg t e m p e r a t u r e precipitat, l(m, i he overall energy of light scattering ia the m e d i u m at any momen, t of t i m e is p r o p o r t i o m d to tit(" int(~l~sity of light scatterittg in any direction. This is easy to see olt summiltg the ('nergy ()f scattered light o~t arty closed surface s aromtd a scattering volume: (4)

E~¢ =~ I s ,I,~ .

H e r e I s is the absolute light int,ensity (m s u r f a c e e h , m e , tt ds. By int,e g r a t m g for lhe sl)here (>f radius r we o b t a i n the result

t

E~(. :..

;

i (O) 2 ~ r r " s i n O d O = 27rr210

0

,

P ( O ) smOdO==27rr"

P (0),I

i ,

. I (O) s i l t O d O : A l

0

(0). (5)

0

I~ this expression P (0) is the flmeti(m of the angular distribution of scattered [ighl, rela, ted to the distributitm of scattering particles according 1o dimettsiol*: I (0) is the abs(duto intensity of light, scattering in the direction of angle 0 to an incident beam at distan('e r from the scattering volume; I o is the intensity of the incide~tt light /)ealn

I (0) P (o) . . . . . . ;

1.

A -2ur ~

f, P (0) s i n 0 d 0 o

1' (0)

1104

V . M . GOL'DBERG: et al.

Thus, observing the imeessary experimelltal requirements there is a direct relation between the intensity of scattered light and the concentration of polymer precipitated from solutio~

Eso

EorAx

EoK~x

1 (0) . . . . . . . . A A A

c.

(6)

The coefficie~t EoKAx/A is the calibration constant of the device for a given chemical system. The calibration constant ir~corporates the ir~tensity of the light source E0, the Beer coastant for a given polsnner-solvent pair K, the solution layer thickness Ax, the distance from the cell to the data refit r m~d the angular distributio~ function of scattered light. All these parameters, except for the last one, are constant, duriI~g precipitation. The last parameter, i.e. f~P(O) sin OdO/P(O) can vary during the experiment owing to the dime~sions of precipitated particles being variable. This may lead to a chai~ge of the calibration constaat of the device, i.e. produce erroneous results. I t is knowr~ that the sensitivity of the interference factor P (0) to variation i~ dimensiorLs of the scatterir~g particles decreases w~th a reduction of the observatiol~ angle of scattering 0 arid with an increase in the wavelength of the light used. Cor~sequently, experimental conditions are optimum with m i n i m u m angle of scattering and m a x i m u m wavelength of the light used. The practical limit of experimental accuracy is here due to loss in the sensitivity of photomultiplication in the long wavelength range of light and to i,~terfererme due to the transient light beam. Replacir~g turbidity measurements from the weakenir~g of transient light beams by measuring the intensity of light scattering helps to increase the sei~sitivity of recordii~g the process by several orders of magnitude, which wide,~s the range of hlvestigation ill the direction of lower polymer co1~centrations. The maiI~ requireme~ts for theoretical accuracy of this method are: l) absence of marked light absorptim~ from the medium, Itrans/Iinc ~- 1, where I denotes the intensity of incidel~t and transient light beams; 2) independence of the distribution function1 of particles according to their dimensions of solution concentration for a given material-solver~t pair. The first condition is ixormally related to the workii~g range of concentrations and in most practical cases can be fulfilled with a sensitive apparatus. The second condition depends more on the chemical rLature of the system (tendency to aggregation, gel formation, crystallization, etc.). The. variatious of relation (6), which are due to deviation from this condition, ilmrease with a reduction in the wavelength of the light used, since in this case the index of scattered light will become more sensitive to a dimensional variation of scattering particles. Temperature conditions of fractionation. Optimum conditions of fractionatior~ by temperature precipitation can be calculated if the rate of precipitation of the polymer from solution and the dependence of the precipitation temperature of the fraction on molecular weight are known. I n a first approximation the rate of precipitation of the polymer with a given molecular weight at the corresponding temperature is proportional to its concentration in solution

dc/dt = -- ke.

(7)

I t m a y be assumed that the rate constant of this process in a n actual chemical system is independent both of polymer molecular weight and of absolute temperature, if it is lower than a certain limit. These assumptions are reasonable since the temperature during precipitation does not vary too markedly and the independence of the constant of precipitation of molecular weight has been verified experimezttally fairly satisfi~ctorily.

T e m p e r a t u r e p r e c i p i t a t i o n as a m e t h o d fin' p o l y m e r f r a c t i o n a t i o u

1105

I t is easy to see t h a t the t i m e of p r e c i p i t a t i o n of a given fraction, or more a c c u r a t e l y a certain p a r t of a given fraction, is simply d e t e r m i n e d by rate c o n s t a n t k. F o r our purposes precipitation of n}~ of a fraction is sufficient, t h e n

At . . . .

i k

In ( 1 - - 0 . 0 I n ) .

(8)

U n d e r ideal conditions of p r e c i p i t a t i o n the t e m p e r a t u r e which eorresponds to the initial p r e c i p i t a t i o n of the fraction is related to the molecular weight by the F i e r y ratio [7]

1 =? 1 + TM

,

(9)

where b is a c o n s t a n t for a givell p o l y m e r - s o l v e n t system; M i s molecular weight; TM is the absolute t e m p e r a t u r e of p r e c i p i t a t i o n of a fraction of molecular weight lli; 0 is the temperature. I n a diN)rential form ratio (9) beeom,'s

TM'b dM dTM = -'2-0-- M--Q; "

(10)

F r o m expressions (8), (10) the m a x i m u m rate of r e d u c t i o n of solution t e m p e r a t u r e which is r e q u i r e d for the p r e c i p i t a t i o n of a p o l y m e r fraction w i t h a g i v e n w i d t h A M / M per n'!/o and t,o a v o i d superposition on subse, q u e n t p o l y m e r fractions can be d e t e r m i n e d

ATM ,St

k TM2b ( A M ~ 1 -- ln(1--O.Ol,~) eo \-=~I-/-~i4-'/-/'

(J~)

or using (9)

k

T~

['V~=--ln(i_0.01n)

(

"20'(0--TM)\~/

AM~ ]

(12)

where IV: is the weight proporti(nt of fraetim~ 1. Tile relatior~s il~dieate t h a t to precipitate tYactions with a eo~staitt w i d t h (AM~M) the rate of coolir~g of the solutio~ at e v e r y m o m e n t of t i m e should be proportio~ml to the differetme b e t w e e n t h e t e m p e r a t u r e of preeipitation mid the 0-point, WT ~ T (O--T). A linear r e d u c t i o n ir~ t e m p e r a t u r e (AT = e o n s t ) has the result t h a t the r e l a t i v e w i d t h of p r e c i p i t a t i n g fractions corresponding to the same t e m p e r a t u r e range ilmreases during the process, i.e. on t r a n s i t i o n from high to low molecular weight fractions. This follows directly from

/ M ]/

1 ~T "--~ (--e\Z~,) "

(13)

The n e x t i m p o r t a n t result is t h a t the o p t i m u m conditions of effective fl'aetionation are d e t e r m i n e d to a large e x t e n t b y t h e absolute rate c o n s t a n t of p o l y m e r p r e e i p i t a t i o a /c from a give~l solution. I f this value is fairly low, fraetionatiot~ w i t h given efficiency m a y t a k e quite a time and the m e t h o d of t e m p e r a t u r e p r e c i p i t a t i o n w i t h separatio~ of fraetioD.s m a y lose sigqdfieal~ce. I n this ease t e m p e r a t u r e precipitatiot~ w i t h o u t separation of fractions has prospects. The m e t h o d involves the followiug: according to (1) the ent ire e(mcentratiou of the p o l y m e r

1106

V. M:. GOL'DBERG et al.

fraction is proportional to the initial, i.e. m a x i m u m rate of precipitation:

C ~

-- ~-

max

I f the rate construct of polymer precipitation from a given solution is knowtx, the conceatratiot~ of all fractions, i.e. MWD can be estimated from the slope of the ki~mtic curve of temperature precipitation in the temperature range corresponding to a certain MWD. The rate of temperature reduction m a y considerably exceed the permissible rates correspo1~ding to conditions of effective separatio~ of fractions. Thus, in this case all subsequent fractions are superimposed over a period of time on former ones and the slope of the kinetic curve of temperature precipitation at each given point represents the superposition of rates of precipitation of polymer fractions, correspoI~ding t~ the appropriate temperature range. The actual initial rates of precipitation of certain fractions, correspo~dii~g to the cmTent temperature, should be calculated by taking this superposition into account. F o r this purpose the curve of temperature precipitation should be separated into the following regioim: the number of ranges and their width depend on the requisite number of fractions and their width. The amount of fraction I is determined from the slope of the kitmtic curve, i.e. i~1 the first range according to (14)

All subsequent fractions are determined by calculation c,,

1 ~dc t

n - l c, e - ' " ° - " '

,

(16)

i=1

where (dcldt)n is the slope o f the k i n e t i c curve, i.e. in the n t h range; t~, t~ are the times o f passage of the boundaries of corresponding ranges. The efficiency of fractionation by this method depends on the method of subdivision of the kinetic curve into ranges; the width of the fractions calculated follows from expression (10)

AM

20

M

T~2b

•M ' / 2 A T .

CONCLUSIONS (1) A critical study was made of temperature precipitation as a method of polymer fractionation. (2) I t was shown that the possibilities of the method can be extended when the intensities of light scattering are recorded at a fixed angle instead of using measurements of the t u rb i d i t y of the medium during precipitation. (3) The principles of calculating optimum conditions of fractionation by temperature precipitation are described. Translated by E. SEMERE REFERENCES

1. S. Ya. F R ENK E L ' , Vvedenie v statistieheskuyu teoriyu polimerizatsii (Introduction to the Statistical Theory of Polymerization). Izd. " N a u k a " , 1965 2. W. C. TAYLOR and Z . H . TUNG, SPE Trans. 2: 119, 1962; W. C. TAYLOR and J. P. GRAHAM, J. Polymer Sci. B2: 169, 1964

Temperature precipitation as a method fro' polymer fraetionation

1107

3. A. I. SHATENSHTEIN, Yu. P. VYRSKII, N. A. PRAVIKOVA, P. P. ALIKHANOV et a/,, Praktieheskoye rukovodstvo po opredeleniyu ]~IV i MVVR polimerov (Practical Guide for Determining Molecular Weight and Molecular Weight Distribution of Polymers). Izd. " K h i m i y a " , 1964 4. R. KONINGSVELD arid A. J. STAVERMAN, ~. Polymer Sei. 6, A-2: 349, 1968 5. L. W. GAMBLE, W. T. W I R K E and T. LANE, J. Appl. Polymer Sei. 9: 1503, 1965 6. P. MOLYNEUX, Kolloid-Z. 226: 15, 1968 7. P. J. FLORY, Principles of Polymer Chemistry. Coi'lmll University Press, Ithaca, N(,~v York, 1953