1、UC678.074: 678.4: 678.7: 620.1 : 678.028 DEUTSCHE NORM March 1983 DIN Testing of rubber and elastomers Measurement of vulcanization Characteristics (curometry) I 53529 Evaluation of cross-linkina isotherms in terms of reaction kinetics Part 2 Prfung von Kautschuk und Elastomeren; Vulkametrie, Bestim
2、mung des Vulkanisations- Verlaufes und reaktionskinetische Auswertung von Vernetzungsisothermen Supersedes October 1972 edition In keeping with current practice in standards published by the International Organization for Standardization (/SO), a comma has been used throughout as the decimal marker.
3、 1 This standard specifies a method of determining the vulcanization characteristics of rubber mixes with the aid of curemeters and of evaluating cross-linking iso- therms in terms of reaction kinetics. A description of the apparatus required is given in DIN 53 529 Part 1 and DIN 53 529 Part 3 deals
4、 with the determination of cross-linking behaviour with the aid of rotorless cureme- ters. The system of evaluation detailed in clause 7 gives a formal description of various stages in the vulcanization process that does not initially account for the underlying reaction mechanisms. Note. The direct
5、proportionality posited between the shear modulus and the cross-linking density is based on the statistical theory of rubber elasti- city (cf. Nitzsche/Wolf: Struktur und physika- lisches Verhalten von Kunststoffen, Berlin, Heidelberg, Vienna: Springer-Verlag, 1962, pp. 234 ff .). It gives the equat
6、ion: G= V. R. T (1) where G is the shear modulus, in N/mm2; v is the cross-linking density, in mol/mm3; R is the universal gas constant, 8.31 J/(mol . k); T is the thermodynamic temperature, in K. If the strain is directly proportional to the force applied, then: r=G. y=v.R.T.y (1 a) where y is the
7、shear strain, equal to the tangent of the T is the shear stress, in N/mm2. If T and y are constant, then T is proportional to v. (1 b Scope and field of application shear angle; 2 Concepts 2.1 Vulcanization See DIN 53 501. 2.2 Cross-linking isotherm At a constant temperature of test, a cross-linking
8、 isotherm is the function of time of that property which serves to measure the course of the cross-linking reaction. In the context of curometry, the cross-linking isotherm is thus the function of time of the oscillating shear force F, or of the curemeter indication proportional to it, occurring at
9、a given temperature as a result of vulcaniza- tion and expressed as: where t is the vulcanization time (see figure 1). F = f (4 (2) t IC O al t Lc I lu W c cn tX Vulcanization time t - Vulcanization time t - Figure 1. Cross-linking isotherm of a rubber mix without (top graph) and with (bottom graph)
10、 the occur- rence of reversion Note. In order to obtain the true cross-linking iso- therm, it may be necessary to correct the values read from the curemeter curve according to the method specified in DIN 53 529 Part 1. Continued on pages 2 to 10 Beuth Verlag GmbH, Berlin 30, has exclusive sale right
11、s for German Standards (DIN-Normen) DIN 53 523 Part 2 Engl. Price group 8 Sales No. O1 08 09.85 Page 2 DIN 53 529 Part 2 2.2.1 Initial value Fa Fa is the minimum of the cross-linking isotherm indicat- ed by the curemeter (see figure 1). 2.2.2 Final value Fo0 FW is the final curemeter indication, con
12、stant in time, on completion of the cross-linking reaction (transition of cross-linking isotherm into a plateau at t -+o0 (see figure 1). 2.2.3 Reversion Reversion may be defined as the condition in which a concurrent decomposition of the macromolecular net- work superimposes itself on the cross-lin
13、king process. As cross-linking and decomposition are concurrent reac- tions when reversion occurs, the curemeter indication does not reach a constant final value, the cross-linking isotherm being characterized instead by a more or less broad maximum (see figure 1). 2.2.4 Maximum value Fmax in system
14、s producing a reverting curve, F, is the maximum of the curemeter indication. 2.2.5 Intermediate value Ft F, is the curemeter indication at any specified time t in the analytical range, .e. tis greater than ti. See subclause 2.3.1 and figure 1 for ti. 2.3 Reaction kinetics The parameters of kinetic
15、reaction for a chemical pro- cess are given by the incubation time, the conversion variable, the reaction order, the conversion rate constant, the activation energy and the conversion time. 2.3.1 Incubation time ti ti is defined as the time elapsing from the start of the test (t = O) until the point
16、 where cross-linking begins. Thus ti is the start-up time immediately preceding the cross-linking reaction. Subclause 7.6 specifies the method of its determination. Note 1. The definition of incubation time given above covers time lapses of both chemical and mechani- cal origin. Whether, in any one
17、case, ti is to be attributed to chemical processes or to the appara- tus used can only be determined by specific testing. fied in DIN 53 523 Part 4 and is not identical Note 2. The scorch time t5 shall be determined as speci- with ti. 2.3.2 Conversion variable x The conversion variable x is directly
18、 proportional to the relative degree of cross-linking and is defined by the equation (3) ct is the concentration of the cross-linking points at c x is obtained from the values of Fa, Ft and Fm accord- ing to the equation: time t; is the final concentration of the cross-linking points (t+w). (4) If r
19、eversion precludes the determination of Fw, then the maximum value F, (see subclause 2.2.4) may be taken as an appropriate substitute for it. The following then applies; where c, signifies the concetration of the cross-link- ing points at time t, 2.3.3 Reaction ordern and conversion rate constant k(
20、n) Conversions that proceed to completion, such as those occurring in the cross-linking reaction where the entire cross-linking agent is consumed, can be expressed over a wide conversion range by: dx dt _- - k(“). (1 - x)“ (t ti) where dx . - IS the reaction rate; dt k(“) is the nth order conversion
21、 rate constant; n is the reaction order in respect of time, .e. n indi- cates the time law (see subclause 7.1) according to which the cross-linking reaction proceeds. Note 1. The following relationship exists between the conversion rate and the reaction rate. The reaction rate is given by the expres
22、sion dc -=kp dt (c,-c,)“ (ttl) where dc . - IS the reaction rate; dt kp) is the nth order reaction rate constant; n is the reaction order in respect of time; cl is the concentration of cross-linking points at time t (iti); c, is the final concentration of cross-linking points (t+). To obtain the con
23、version rate, .e. the variation of the conversion variables x with time, the equa- tion is transformed as follows: - kp). can- . (1 - x)“ (t ti) (6a) d(z) - dx dt dt The product kp). c, as the conversion rate constant kc“), so that: is collected and defined dx dt _- - k(“). (1 - x)“ (t ti) According
24、 to subclause 2.3.2: thus: or, for systems with reversion: DIN 53 529 Part 2 Page 3 n and h(“) are calculated as specified in sub- clauses 7.4 and 7.5 respectively. laws referred to above, the reaction order n is of only formal significance if the chemistry of the cross-linking reaction is otherwise
25、 unknown. In particular, it should be noted that the reaction order n cannot be directly equated with the molecularity of the cross-linking reaction. The occurrence of fractional reaction orders (n * O, n * 1, n * 2) indicates that composite reactions, such as parallel or consecutive reac- tions, ha
26、ve taken place. Strictly speaking, such reactions are governed by a rate law that differs from the general rate law; for chemical engi- neering purposes, however, the power law of the cross-linking reaction permits sufficiently accurate calculations of the course of the cross- linking isotherm. Note
27、 2. In the general rate law and the relevant time 2.3.4 Activation energy EA In chemical reactions, the activation energy EA is the specific constant determining the energy required to activate the reaction and thus also determines the tem- perature dependence of the rate constants. EA is calculated
28、 on the basis of the equations given in subclause 7.8. 2.3.5 Conversion time (vulcanization time) t, Conversion, or vulcanization time t, signifies the time elapsing between the start at t = O and conversion x. The conversion time t, is calculated on the basis of the equations given in subclause 7.7
29、. 3 Principle of method Curemeters, giving one set of measurements per speci- men tested, permit the course of the cross-linking re- action occurring at constant temperature, i. e. the cross- linking isotherm, to be recorded; the course of the reaction may then be characterized by an evaluation of t
30、he cross-linking isotherm in terms of reaction kinetics. Given constant temperature, the cross-linking isotherm is the result either of the variation of the shear modulus with time or of a measurand that is proportional to it. The measurand may be a force, a torque, or a linear or angular amplitude.
31、 Comparable results can only be obtained from the evalu. ation of cross-linking isotherms when the curemeter has been checked in respect of reaction kinetics according to the method given in clause 8. 4 Designation of the method Designation of the method of determining the vulcaniza- tion characteri
32、stics of a rubber mix and the evaluation of the cross-linking isotherm in terms of reaction kinetics as specified in this standard (A): Test DIN 53 529 - 02 - A 5 Specimens and specimen preparation The specimen shall be a vulcanizable rubber mix kept in a sealed airtight container at temperatures no
33、t exceeding 23OC for at least one hour, but for not more than 72 hours, prior to the test. For inter-laboratory tests, details of storage conditions shall, if required, be subject to separate specif ication. Specimens shall be taken either by cutting, punching or boring, and the choice of dimensions
34、 shall ensure that the specimen occupies the entire volume of the reaction cavity of the apparatus used. 6 Procedure Vulcanization testing shall be performed in curemeters complying with the requirements laid down in DIN 53 529 Part 1. Temperature and frequency shall be specified separately. Once th
35、e test has started, the specimen shall be brought as rapidly as possible to the test temperature and sub- jected to an alternating stress produced by mechanical oscillation of largely constant amplitude. The specimen shall either be given a linear or angular amplitude to cover, the force or torque w
36、hich that requires as vulcani- zation proceeds being the quantity measured, or it shall be subjected to a given force or torque amplitude, and the resulting strain (displacement, angle) measured. The shape of the specimen, the type of load applied, the drive and measuring systems may differ accordin
37、g to the type of curemeter used. 7 Evaluation 7.1 Timelaws By integrating the rate law given in subclause 2.3.3 (equation 51, the conversion variables x as a function of time are obtained, i. e. the time law of the cross-linking reaction. Reactions of the first order (n = 1) give either the time law
38、: or: in(i-x)=-P). (t-t,) (9) ig (1 - x) = - M in (1 - x) = - k(). (t - t,) (9 a) M = lg e = 0,4343 Note 1. For n = 1, the reaction rate constant kS1) and the conversion rate constant k(l) are identical, since, following note 1 to subclause 2.3.3: kv)= k“. c 1-1 = k“ If a different time law applies,
39、 i. e. n * 1, then the following is obtained: 1 1 1-n i-n Time t shall be measured in minutes. Note 2. The significance of the conversion variable 1 - x occurring in the time law is given by the following consideration. Consistent with its definition in subclause 2.3.2, the relative degree of cross-
40、linking measured by the conversion variable x is x = O at the start of cross-linking, so that 1 - x = 1; at the end of the cross-linking reaction x: = 1, and thus 1 - x = O. 1 - x is therefore a decreasing function of time. cm I (1 - x)l-n= - k(“). (t- ti) + - (1 0) -. 7.2 Determination of the final
41、 value FCO If, when the vulcanization process is completed, the cross-linking isotherm runs virtually parallel with the time axis, then FCO is the final deflection of the cure- meter, independent of time. Page 4 DIN 53 529 Part 2 -1 - f Figure 2. Determination of the final value from the indicated v
42、alues of one cross-linking isotherm (top graph) and of a family of cross-linking isotherms at test temperatures Tl, T, and T3 (bottom graph) In figure 2 F is the curemeter indication; T is the test temperature; t is the vulcanization time. If it is not possible to obtain a reliable reading for FCQ d
43、irectly from the cross-linking isotherm, then FCQ - Fa may be determined according to the method given here by way of example. Lg (F, - Fa) is plotted versus the reciprocal of the test time l/t and an attempt is made to find F- - Fa by extrapolating to the ordinate (see figure 2). If the method desc
44、ribed above is applied to the evalua- tion of a family of cross-linking isotherms (parameter: temperature T), then FCQ - Fa can be determined with even greater reliability. As long as the alteration of Fm with temperature remains insignificant, curves are ob- tained that can be more easily extrapola
45、ted at 1 /t = O to the ordinate point Lg (Fm - Fa). They intersect with the ordinate (t+m) at lg (Fw - Fa) (see figure 2). 7.3 Determination of Fmax When reversion takes place, Fmax is the highestvalue indi- cated by the curemeter. Note. Errors made when determining FW influence the values obtained
46、for ke) and n. The value Fmau, which is introduced as a substi- tute for Fm when reversion prevents the latter value being obtained, does not lead to the true time law of the cross-linking reaction, but it does enable an approximate calculation to be made of the vulcanization process in reverting sy
47、stems. 7.4 Determination of the reaction order n Cross-linking reactions can frequently be described by the time law of the first order (n = 1). It is thus recommended that the cross-linking isotherm be evaluated initially according to the method given in subclause 7.4.1. Should it become apparent t
48、hat a dif- ferent time law must apply (n * I), then evaluation shall continue according to the procedure specified in sub- clause 7.4.2. 7.4.1 Cross-linking reaction of the first order (n = 1) At different times during the test (tG), the conversion variable x is determined according to the equation
49、and g (1 - x) is plotted versus the test time. If n is equal to 1, a falling conversion line is obtained as demonstrated in subclause 7.1. It intersects the time axis at ti (see figure 3). As set forth in subclause 7.5.1, the slope of the conver- sion line is used to determine the conversion rate constant k(l), which in this instance is identical with the reaction rate constant k;) (see note 1 in subclause 7.1 1. x=o ti t n=-1 from n = 1 Figure 4. Conversion curve for n = 1 and deviations (1-XI DIN 53 529 Part 2 Page 5 7.4.2 Cross-linking reaction of the nth order (n * 1)
