A kinetic model for heterogeneous acetalisation of poly(vinyl alcohol)

Eur. Po(vm. J. Vol. 20, No. 3, pp. 257 263. 1984 Printed in Great Britain. All rights reserved

0014-3057/84 $3.00+0.00 Copyright (( 1984 Pergamon Press Ltd

A KINETIC MODEL FOR HETEROGENEOUS ACETALISATION OF POLY(VINYL ALCOHOL) P. RAGHAVENDRACHAR a n d M. CHANDA Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India (Received 24 May 1983)

Abstract--A model for heterogeneous acetalisation of poly(vinyl alcohol) with limited solution volume is proposed based on the grain model of Sohn and Szekely. Instead of treating the heterogeneous aeetalisation as purely a diffusion process, as in the Matuzawa and Ogasawara model, the present model also takes into account the chemical reaction and the physical state of the solid polymer, such as degree of swelling and porosity, and assumes segregation of the polymer phase at higher conversion into an outer fully reacted zone and an inner zone where the reaction still proceeds. The solution of the model for limited solution volume, moreover, offers a simple method of determining the kinetic parameters and diffusivity for the solid-liquid system using the easily measurable bulk solution concentration of the liquid reactant instead of conversion~listanee data for the solid phase, which are considerably more difficult to obtain.

NOMENCLATURE

C0 CAs

CAo CAm

CA(t)

c...,c~.., c. D D~ k m

P,Q ro r~ r~, rc l) rc n

R R0 Rm t Ii VAs

v x

x z

parameter defined by equation (55) stoichiometric coefficient in equation (6) formaldehyde content of polymer phase, (g CH20 ) (g dry PVOH)c at surface of polymer phase concentration of liquid reactant A in solid phase, mol cm- 3 concentration of liquid reactant A in the bulk initially, mol cm 3 concentration of liquid reactant A at the boundary between reaction and diffusion zones, mol cm -3 concentration of liquid reactant A in the bulk at time t, mol cm -3 concentration of liquid reactant A in zone I and zone II of solid, respectively, mol cm -3 initial amount of solid reactant B, mol diffusivity, cm: hr- i effective diffusivity of liquid reactant in solid phase, cm 2 hr first order surface reaction rate constant, cm hrparameter defined by equation (13) parameters defined by equations (3) and (4) half thickness of grain, cm position of moving reaction front in individual grains, cm r¢ at time t = t~ position of moving reaction front in grains of zones I and II, respectively, cm distance parameter in solid, cm distance of solid (sheet) surface from a reference plane in the solid, cm distance of boundary between zones ! and II from the reference plane in solid, cm time, hr time required for complete conversion of the surface of solid, hr local rate of reaction of liquid reactant A in solid phase, molhr ~cm 3 volume of bulk liquid phase, cm 3 local conversion of the solid average conversion of solid £at t=tl distance from the surface of rolled film, cm parameter defined by equation (54) 257

Greek letters E porosity of solid PB molar density of PVOH, molcm 3 a reaction modulus (dimensionless).

1. INTRODUCTION Heterogeneous reaction is i m p o r t a n t for the production of poly(vinyl acetals). It is well suited for specific purposes such as acetalisation of poly(vinyl alcohol) [PVOH] fibres a n d films which have imp o r t a n t commercial applications. Acetalisation of outer layers of films a n d fibres imparts to them high resistance to water. The reaction is carried out by steeping the fibres or films in b a t h s c o n t a i n i n g water, salts like sodium sulphate, mineral acid catalyst a n d the required aldehyde. M o s t o f the earlier studies o n acetalisation kinetics are experimental a n d are limited to the d e t e r m i n a t i o n o f overall conversions for various reaction conditions. The h e a t - t r e a t m e n t t e m p e r a t u r e o f P V O H , c o m p o s i t i o n o f acetalisation bath, a n d reaction temperature are the usual variables in these studies [1-4]. S a k u r a d a a n d N a k a m u r a [5] reported t h a t the rate of formalisation increases with decreasing a m o u n t s of anti-swelling agents. They also f o u n d t h a t the rates increase as the h e a t - t r e a t m e n t t e m p e r a t u r e decreases [2]. These observations show t h a t the overall reaction rate is related to the degree to which P V O H swells under the conditions o f reaction. W h e n the solid swells to a higher degree, the diffusional resistance inside the solid decreases due to increased porosity a n d the reaction rate increases. Factors like the presence o f anti-swelling agents, high h e a t - t r e a t m e n t t e m p e r a t u r e s a n d low reaction t e m p e r a t u r e s decrease the swelling a n d thereby the reaction rates. The mobility o f aldehyde in the swollen P V O H is also expected to affect the overall rate a n d distribution of acetal groups in the solid. Thus, a low molecular weight aldehyde can diffuse deeper into the solid a n d react with a larger volume, p r o b a b l y with higher overall reaction rates. Emets a n d A k i m [4] for

258

P. RAGHAVENDRACHARand M. CHANDA

example reported that, when fibres are acetalised with different aldehydes, the degree of acetalisation for a given time decreases in the order: HCHO > PhCHO > nitrofuryl acrolein. Matuzawa and Ogasawara [6] obtained rate data on the formalisation of PVOH film by employing a rolled film technique which involved tedious and difficult experimentation. A rolled film of PVOH was withdrawn from the formalisation bath after specified times and sliced into layers. The formal contents (conversions) of these layers were determined by the chromotropic acid method [7] and conversiondistance curves were plotted. The theoretical analysis given by Matuzawa and Ogasawara [6], based mainly on the kinetics of dyeing, assumes the heterogeneous acetalisation to be purely a diffusion process, described by the nonsteady-state diffusion equation. Such an assumption may be appropriate for dyeing of polymer films where chemical reactions are generally absent, but in the case of reacting systems, and especially at high conversions, it would not be valid. For example, in the dyeing of nylon-6,6 with naphthalene scarlet 4R (C.I. Acid Red), which may be considered as a reacting system in view of an approximate relation between the uptake of the dye and the number of terminal amino groups in the polymer, the concentrationdistribution curves show two regions at higher conversions [8], namely, an outer saturated region where the concentration of the absorbed dye is constant and an inner diffusion zone where the concentration decreases gradually towards the interior. The unsteady-state diffusion equation cannot describe such conversion--distribution in the solid. A realistic model for heterogeneous acetalisation should evidently take into account both diffusion and chemical reaction. In addition, it should take into consideration the relevant structural features of solid PVOH, such as the degree of swelling and porosity. Among several models that have been proposed for reacting porous solids, the grain model appears more attractive. Since its development by Sohn and Szekely [9] the model was tested and found consistent with experimental data in many cases of gas-solid reactions. A major advantage of the grain model is that it allows interpretation and correlation of experi-

u

o

u

u

u

M

nLlnumununumun

mental data for porous solids under conditions of chemical or mixed control and enables prediction of overall reaction rates for various solid structures. The grain model, though derived originally for gas-solid reactions, is applied for the first time in the present study to heterogeneous acetalisation of PVOH by liquid reactant and solved for the practical case of limited solution volume where the liquid reactant concentration decreases with time due to reaction. 2. M O D E L

DEVELOPMENT

2.1 Basic assumptions The grain model considers the solid pellet to be a compaction of a large number of small non-porous solid particles called "grains". The reaction proceeds in the grains by shrinking core mechanism. The liquid reactant diffuses through the space between the grains and reacts with the solid simultaneously. When both chemical reaction and diffusion control the overall rate of reaction the reaction is faster at the external surface of the pellet. The period (fl) required for the complete conversion of the surface is called the first stage of the reaction. In the second stage of the reaction, at any time t > tt, there will be two zones in the pellet, viz. the completely reacted outer zone and a partially converted inner zone (Fig. 1). In applying the above grain model to acetalisation of PVOH sheet by liquid-solid reaction, the swollen PVOH sheet is assumed to be a compaction of a large number of solid particles. The absorbed water and acid fill the space between these particles and act as a medium for aldehyde transport. The grains in a solid are generally not uniform either in shape or in size and in the case of PVOH, moreover, the shape and size are likely to change with reaction conditions. It is however assumed for mathematical simplicity that all the grains are identical and resemble flat plates, an assumption which is equivalent to assuming that the local rate of reaction within the sheet is independent of the local extent of conversion, as long as the solid reactant is present. Other assumptions are as follows. (a) The pseudo steady-state approximation is appropriate for describing the concentration of aldehyde within the sheet.

u u LI u u M OnOnOnOnOnl).l nunumumununull

on uun unn uU nDl l lxl l ol , I I | l | l

1.0 t<~ x v

•

§

=

I

/

0.5

o .J

0

Zone

I Z o n e IT I

I I 1.0

R/R °

I

0

1.0 R/R

o

0

t.O R/R

o

Fig. 1. Progress of reaction in flat pellet consisting of flat grains (schematic).

259

Heterogeneous acetalisation of PVOH (a)

(b) The resistance to liquid-solid mass transfer is negligible. (c) The solid structure is macroscopically uniform and is unaffected by the reaction. (d) Diffusion within the sheet is equimolar counter diffusion. (e) The effective diffusivity of aldehyde is uniform throughout the sheet. (f) The viscous flow contribution to mass transport in the pores is negligible. (g) The reaction is irreversible. (h) The rate of surface reaction in grains is first order with respect to aldehyde concentration. Assumptions (a) to (d) are valid in the experiments of Matuzawa and Ogasawara, because (1) very low formaldehyde concentrations were employed; (2) the reactor was well agitated; (3) information available in literature indicates no structural changes in PVOH; and (4) one mole of formaldehyde on reaction produces one mole of water. It is also known that formalisation is irreversible at low acid concentrations. Since intermolecular acetalisation is possible in solid PVOH, the isolation of hydroxyls is not considered and a simple rate equation is used for the surface chemical reaction. The grain model was originally derived for gas-solid reactions. In applying this model to liquid-solid reactions, care must be taken to ensure the validity of two of the assumptions made in the model, viz. pseudo-steady-state and constant ambient conditions. Lindman and Simonsson [10], in their analysis of the application of the shrinking core model to liquid-solid reactions, have demonstrated that the pseudo-steady-state assumption is justified even for highly concentrated liquid solutions. The normally employed aldehyde concentrations in heterogeneous acetalisations are however quite low and the pseudo-steady-state assumption should be valid. Also, when a large molar excess of aldehyde is used in acetalisation, as by Matuzawa and Ogasawara [6], the bulk concentration of aldehyde can be assumed to be constant. 2.2 Grain model with constant ambient conditions The solution for the case of a slab like pellet consisting of fiat grains was obtained by Sohn and Szekely [9]. The same solution is applied here to the experimental data of Matuzawa and Ogasawara [6]. These data pertain to the first stage of reaction, i.e. for the period before the external layer of the solid is completely converted. For this period, the conversion--distance relationship is given by [9] f x -

/1

--E

kkl/2"l

t

(1)

(

\
Experimental

6

> a_ o, O N T

5 4

%

I

o

2

13

3

~

4

o

7

z I

0

e~ 20 no

x

0

20

g) Distance

x 200

30

(cm)

Fig. 2. Comparison of grain model predictions (solid line) with experimental data (points) of Matuzawa and Ogasawara [61. where

P =

bk

Paro

Cgot /cosh

{R {1 - '

ky'Z~

°t D, ro)

J

(3)

and 1 --

E

k ~ I/2

Q = -~-¢ ro/

(4)

The constants P and Q are evaluated using Marquardt's algorithm. D c values calculated by assuming reasonable values for E and PB are in the range 10 -6 - 10 -8 cm 2 sec l, normally expected for diffusion in swollen polymers. The calculated conversion-distance curves in Fig. 2 show that the agreement between the model and the experimental results is satisfactory. An important parameter in the grain model is the reaction modulus tr defined as

I

(2)

•

O

a = R { 1 - E k~ 1/2

\ D< ro) J

The stoichiometric coefficient b is 2 for acetalisation of PVOH. In the experiment of Matuzawa and Ogasawara [6], the sheet (rolled film) was closed on one side preventing diffusion from that side. This side is taken as the reference plane. The experimental conversion data are fitted to the expression x = P cosh(QR)

7!

(5)

= Q~

The reaction modulus incorporates both kinetic and structural properties and is a measure of the relative magnitudes of chemical reaction and diffusion rates. As a approaches zero, pore diffusion presents negligible resistance to progress of the reaction. Under this

260

P. RAGHAVENDRACHARand M. CHANDA where CAs is the concentration of A on a plane at a distance R (R < R0) from the central reference plane in the sheet; De is the effective diffusivity of A and VAs is the local rate of consumption of A in moles per unit volume of porous solid per unit time. The rate of disappearance of solid reactant in a grain is given by

075

COrc -PB ~ - = b kCAs

Ix ,~ 0.50

(8)

VAsis given by 1--E

VAs=

L ]/

II.

012.~|/

"rrr v=¢o

I/

c,(,...._~, vs CA(o)I

I/

V 0

I I00

t(hr)

(9)

CAs = CA(,), R = R 0 (surface)

(10)

COCAs~dR= 0, R = 0 (central plane)

(11)

and

Fig. 3. Model predictions of solid conversion vs time and bulk phase concentration of aldehyde vs time for heterogeneous formalisation of PVOH sheet. Assumed reaction conditions: R0= 0.02 cm, m = 70.0 cm i, CA0= 7 x 10-4molcm 3, pB=0.03molcm-3' k/r0=0.9hr-t.

yields C cosh(mR) A(,)~

CAs = condition, the conversion is uniform throughout the solid. As a approaches infinity, the reaction occurs mostly in a narrow zone between the unreacted core and the completely reacted layer. The smallest and the highest values of tr thus correspond to the asymptotic solutions for pure chemical reaction control and pure diffusion control respectively. The values of tr calculated from the experimental data of Matuzawa and Ogasawara [6] are in the range 3-6. These values are relatively large indicating a strong resistance to diffusion. This is also evident from the rapid decrease of conversion towards the interior of the sheet (Fig. 2). The reaction modulus decreases and more uniform conversions in the solid are obtained if the sheet is highly swollen or a very thin sheet is used. In view of the good agreement obtained between the model and the experimental data under different reaction conditions, the grain model may be considered as satisfactory for heterogeneous acetalisation of PVOH. 2.3 Grain model with changing ambient conditions The grain model is solved for the case where the liquid reactant concentration decreases with time due to reaction. The acetalisation is represented by A(1) + bB(s)--, C(l) + D(s)

k Cgs

where E is the porosity of the solid (and this may include the volume of inerts, if present). Substituting for VAs and solving equation (7) with the boundary conditions

t

50

(6)

Plane geometry is assumed for the PVOH sheet and the grains. A diffuses from liquid through both sides of the sheet and the diffusion through edges is neglected. Other assumptions are the same as those given in Section 2.1. 2.3.1 The first stage of reaction. A material balance for the liquid reactant A in the PVOH sheet can be written as

(12)

where

_ { 1 - - E k ) ~/2 m - \---D-~-~0,/

(13)

and therefore, tr = mR 0

(14)

Substituting for CAs from equation (12) into equation (8) and solving with the initial conditions

r¢=r o, t = 0

(15)

provides the relation

(ro- re) - bk cosh(mR) f / PB cosh(a)

CA(0dt

- - VAs = 0

(7)

(16)

where 2r0 is the thickness of the grains. The dependence of CA(t) on t can be obtained from the overall material balance for A. The material balance equation can be written as V[CA0 -- CA(0I = CBY/b

(17)

This equation is valid when the bulk volume is large compared to the total pore volume, which usually is the case. ~ can be obtained as an average of the local conversion x in the sheet. Thus,

:'R0 ('~0 Y = | x d R / | dR j0

(18)

jo

Since x = (% - rc)/% for fiat grains, we obtain from equations (16) and (18) 1 bk tanh(a)

CO2Cgs D e~

r0

V = 7 0 0 cm 3

-~ --

r0 Pa

--

a

J0

CA(0 d t

(19)

Heterogeneous acetalisation of PVOH Substituting for £ and rearranging equation (17) gives CA(0 = CAo

CB k tanh__(o) V rop s a

CA(odt

The matching conditions are CA~, = Cas,, = CA~

(20)

t = 0

gives tanh(o) kCs ) ~ Vr~-~at ;

CA(,) = CA0 exp

(21)

Now the concentration profile of A in the sheet and the local conversions in the solid can be obtained as tanh(a) kCst~cosh(mR) a VroPsJ cosh(a) (22)

CA~ = CA0 exp

at

R = Rm

(33)

and

Differentiating equation (20) with respect to t and solving for CA(,) with the initial condition C a < . = CAo,

261

at

dCas,/dR = OCAs,,/OR

R = Rm

where R m is the position of the boundary between the two zones and CAm is the concentration of A at Rm. The concentration distribution of A in the sheet can be obtained from equations (26), (28), (29) and (33) as cosh (mR) CAsl = CAm cosh(mRm)'

CA$1I

0 ~< R ~< R m

Ro - Rm

(23) CAm --

CA(t) [m (R o - Rm) tanh(mRm) + 11

(24)

--

ro

The overall conversion of the solid at t = t~ is given by Vb tanh(a) 2, = Css [CA0 - CA(,,)I = - - a

(25)

2.3.2 The second stage o f reaction. As the reaction progresses, two zones appear as shown in Fig. 1. The material balance equations, the boundary and initial conditions for the second stage of reaction are as follows:

(37)

The variation in solid conversion in zone I is obtained by substituting for CA~, from equation (35) and solving equation (27). This yields re, - re, _ bk

- - - -

(36)

F r o m equations (34-36), one obtains

The time required for complete conversion of the external layer, i.e. for the end of the first stage of reaction, is obtained by substituting for CA(,) from equation (21) and x = 1 at R = R o in equation (23) and solving for t~ to yield t a n ~ ( ~ In

(35)

(R - Rm)CA(t) -+-(R 0 - R)CAm '

P~ ~< R ~< R0

and cosh(mR) V x = b e sinh(a) CB (CAo-- Ca(,))

(34)

f(

cosh

psro

(mR)

CA(t)dt , m (R0 - Rm) sinh(mRm) + cosh(mRm)

(38)

where re, is the grain core position at t = 6- The integration in equation (38) requires the relation between t, Rm and CA(,). The relation between t and R m can be found as follows. Substituting x = (ro - rc)/ro and t = t I in equation (23) and simplifying, using equation (25), one obtains cosh(mR) (ro - rc~) = ro - cosh(~)

(39)

Zone I 0 2 CAsl

(26)

De 0R 2 --VAs=0

Substitution for ( r e , - re,) from equation (38) and for ( r 0 - re,) from equation (39) into equation (40) ro - re, = (ro - r~,) + (re, - re,)

Orc I

-- P a ' ~ = b k Casl 1--e /)As ~---- ro

0CA~I=0, dR

(27)

k GAs I

R=0

(28)

(29)

(40)

and rearrangement of the terms then yields

r0--ro,--r0

cosh(mR)]/fbk

....

]

j

't CA(,)d t = ,, [m (R 0 - Rm) sinh(mRm) + cosh(mRm)]

(41)

Differentiation of equation (41) with respect to t yields at R = R~,, i.e. re, = 0

Zone H 0 2 CAsi I = 0

(30)

OR z r~. = 0 CA~. = CA(O,

mrop B tanh (mR,,) dRm bk cosh(mRm) dt

(31)

g=R0

CA(t)

(32)

- m (R0 - Rm) sinh (mRm) + cosh(m Rm)

(42)

262

P. RAGHAVENDRACHARand M.

Rearranging,

dt

Substituting for CAt,) from equation (50) into equation (43) and denoting the RHS as F(Rm), equation (43) can be rewritten as

mpBro

dR m ×

bk [m (R 0 -- Rm) sinh(mRm) + cosh(mRm)] tanh(mRm) cosh (mR m)

t>t~ f[m ro - rc, dR / I R° dR ~

ro

fRmro--r¢,d R

RoJ0

r0

1 f"~ro--rc,

=~J0

r0

(44)

dR

1 ('Rmre ~ _ r ¢ , d R

+~J0

(45)

r0

Jo

ro

~ cosh (o')

1 fRmr¢,-r~,dR = bk sinh(mRm ) Ro J0 ro pBrotr

f t tl

CAtt)dt [m (R0 -- Rm) sinh(mRm) + cosh(mRm)] (47)

The integration in equation (47) can be performed by writing dt as (dt/dRm)dRm and substituting for dt/dR m from equation (43). Equation (47) thus becomes

x

b

tanh(mR m)

3. APPLICATION OF THE MODEL

The mathematical solutions obtained above for the grain model with changing ambient conditions suggest a simpler experimental procedure to determine the parameters k/ro and De. Thus, instead of obtaining the conversion~listance data for the solid, requiring difficult and time consuming experiments, the concentration of the liquid reactant A in the bulk phase can be measured as the reaction proceeds. During the first stage of the reaction, the decrease in concentration is rapid and exponential. Assuming that the first few concentration-time data are obtained during this period, an exponential relation such as equation (54) can be fitted to these data Z = exp(-at)

(54)

where

VropB

(49)

and then from equation (17) CA(,)-~-'~{~-~-~ - C A 0 - -CB

(53)

This completes the solution. Figure 3 shows theoretical conversion-time curves calculated from equations (49) and (52) and concentration-time curves calculated from equations (50) and (52) for PVOH formalisation by choosing approximate values for the parameters using the data of Matuzawa and Ogasawara [6] and other relevant information.

tanh (tT) kCB a = - --

Combining equations (44), (46) and (48), one obtains Rm

0 ~
and

_ sinh(mRm) { 1 1 }(48 ) ~cosh (-mRm) cosh (a)

R 0-

cosh(mR) cosh(mRm),

Z = CA(t)/CAo

1 fRm re, -- r~, dR - -sinh(mRm) Rodo/ ro Ro x f Rmtanh(mRm) JR0 eosh(mP~) dR~

£

F(Rm)dR m (52)

3.1 Evaluation of kinetic parameters (46)

Again, substitution for (rc,- rc,)/ro from equation (38) in the second term of RHS of equation (45) and subsequent integration with respect to R yields

x

f2m

x = 1, R m ~ R <.R o

Substituting for ( t o - rc,)/ro from equation (39) and integrating, the first term on RHS of equation (45) becomes 1 ~' Rm ro _ re, dR - sinh (mR m)

(51)

For any Rm, the corresponding £, CAt,) and t can be obtained from equations (49), (50) and (52), respectively. The local conversions in the pellet are given by

Jo

The first term of RHS of equation (44) is the contribution of zone II to the overall conversion, while the second term is the contribution from zone I. Using equation (40), the second term is rewritten as

l

t = tl +

(43)

The dependence of CAt,) on time t can be determined by considering the fractional conversion £ at time

fi~ - R° - Rm

dt/dRm = V(gm) from which

CA(t) x

CHANDA

tanh(mRm)} (50)

(55)

Since equation (54) is valid only up to tl, the Z - t curve would deviate from the experimental CA(o/CAo VS t curve beyond fi, when extrapolated to longer times. Thus the point at which these two curves begin to deviate can be obtained. This is illustrated in Fig. 4 using model predicted curves for different assumed conditions of formalisation. From CAtjCAo thus obtained, the conversion £ and the reaction modulus ~r can be calculated from equation (25). Substituting the value of a in equation (55), k/r o can be evaluated and, from the known values of k/ro and t~, the effective diffusivity D e can be calculated.

Heterogeneous acetalisation of PVOH IO

263

1.0 ~

- - V S CA(t)

t

t

CA o I

0.75

vst

Z

o

0.5

\ ~

\\

05

x

o

0.25

I. Ro =005 ]]I. Ro=O.O05 cm 0

20

I

200 Time

n" Ro=O.02 cm I

I

IO0

I

I

40

60

I

I

8O

I00

I

~0

I

40O

(rain)

Fig. 5. Parameter estimation from limited liquid volume experimental results. ( ) Theoretical, (---) Z vs t extrapolated, ( 0 ) experimental points.

Time ( hr )

Fig. 4. Graphical method for determination of t r Assumed conditions of heterogeneous formalisation: m = 70.0 cm-i, ps=0.03molcm-3, CB=0.25mol , CA0=7x 10-4tool cm -3,k/r0=0.9hr I, V = 2 0 0 c m 3. 3.2 Experimental verification An accurately weighed sheet of PVOH was kept immersed in an aqueous bath of 4.8% (w/v) NaCI and 33% (w/v) HC1 at 50 _+0.5 ° for about 2 h r and reweighed after drying the external surface. The dimensions of the swollen sheet were also measured. The porosity of the sheet was calculated from the volume of the sheet and the a m o u n t of water absorbed. The same PVOH sheet was then transferred to a stoppered flask containing an aqueous solution of NaC1 and HCI at 5 0 _ 0.5 °. After equilibrating for about 30 min, a measured a m o u n t of formaldehyde solution was added to start the acetalisation. Small aliquots ( ~ 0 . 0 4 c m 3) of solution were withdrawn from the bath at intervals and formaldehyde was estimated colorimetrically by the chromotropic acid method [11]. The concentration-time data thus obtained are plotted in Fig. 5. The parameters were estimated by the method described in Section 3.1. However, in order to locate the end-point of the first stage of reaction more precisely, an iterative procedure was used to determine CAm)/CAo and tl. The values of tr, k/r o and D e thus determined are 3.77, 1 . 9 2 8 × 1 0 2sec ~ and 1.22× 10 6cm2sec ~. They are in the acceptable range. Also as can be seen from Fig. 5, the predicted concentration-time curve fits the experimental data satisfactorily. 4. CONCLUSIONS The heterogeneous acetalisation of PVOH has been treated, for the first time, as a liquid-solid reaction occurring in a porous solid. The structural properties of solid PVOH such as swelling, porosity and the presence of inerts (crystallites) are considered in selecting an appropriate model to describe the kinetics of acetalisation. The grain model with fiat grains

is tested with the experimental data of Matuzawa and Ogasawara and is shown to describe the kinetics well, both qualitatively and quantitatively. The model is then extended to the case where the concentration of aldehyde in the liquid phase decreases significantly due to reaction. A simpler method which eliminates the analysis of solid and needs measurement of only the bulk phase concentration of the liquid reactant for evaluation of rate parameters is described. The information available on heterogeneous acetalisation is however scanty; important aspects such as the structure of swollen polymeric solids, transport of solute molecules in such solids, accessibility of crystallites for reaction, and the true chemical reaction rate in the presence of inter- and intramolecular reactions, etc. are not well understood. Definitive conclusions and development of more sophisticated models for heterogeneous acetalisation have therefore to be deferred until more detailed experimental results are available. REFERENCES

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