научная статья по теме ON RHEOLOGY, CURE KINETICS AND CHEMORHEOLOGY OF GUM RUBBERS Физика

Текст научной статьи на тему «ON RHEOLOGY, CURE KINETICS AND CHEMORHEOLOGY OF GUM RUBBERS»

ON RHEOLOGY, CURE KINETICS AND CHEMORHEOLOGY OF GUM RUBBERS

© 2010 r. Arpita Mitra" and Arkady I. Leonov4

a Corning Incorporated, Corning, NY, USA b Department of Polymer Engineering, the University of Akron, OH, USA e-mail: leonov@uakron.edu

Abstract—The paper presents an experimentally supported modeling approach, which describes the rheolo-gy, detailed cure kinetics, and chemorheology of a gum elastomer in course of sulfur accelerated vulcanization. Changes in the rheology during cure reaction are correlated with degree of cross-linking, described by vulcanization kinetics. Oil extended SBR exemplifies the approach.

1. INTRODUCTION

Occurrence of cross-links in the course of vulcanization can change the physical state of gum elastomers from viscoelastic liquid to viscoelastic solid. While the rubber viscoelastic properties simultaneously change in the course of reaction, a molecular network, with equilibrium modulus emerge during cure reaction only after the chemical gelation. The approach of this paper consists of the three steps: (i) description of viscoelastic properties of elastomer before vulcanization,

(ii) detailed chemical kinetics of cure reaction, and

(iii) chemorheological studies, which correlate changing rheological properties with the degree of crosslink. Modeling these steps is compared with experimental data.

The paper is organized as follows. The Section 2 describes the tested material, an oil extended SBR, regimes of its vulcanization, methodology, and equipment used in experiments. The Section 3 exposes rheological properties of uncured SBR. The well-known continuum/ thermodynamic theories [1, 2] are used here for the rheological modeling. The Section 4 describes the chemical kinetics of sulfur accelerated vulcanization, its mathematical modeling and comparison with experimental data. This description follows previous papers [3, 4] developed and tested for filled rubbers. We did not review more rough kinetic models employed in literature, as they have been discussed in these papers. The Section 5 displays the chemorheological modeling using the approach [5, 6] developed for filled rubbers. In this paper, the gelation point is determined by employing the existence of linear viscoelasticity for SBR compound, which is absent for filled rubbers because of the Payne effect. More detailed results of this research can be found in Ref. [7].

2. EXPERIMENTAL Material Characterization

Oil-extended styrene-butadiene copolymer

SBR1712C (Goodyear Co) with Mw = 2.2 x 105 and oil content 37.5 phr was used in our experiments. It contained standard curatives: zinc oxide (5.6 pHR), stearic acid (2 pHR), antioxidant (2 pHR), sulfur (2 pHR) and accelerator (1 pHR). A common mixing protocol [7] was used. In pre-cured rheological studies, the SBR was employed without curatives, while the "productive," curative containing samples were used in the following chemorheological experiments.

Rheological Experiments and Equipment

(i) Linear dynamic tests were performed using RMS 800 at 1% strain in frequency range ra = 10-2 to 102 rad/s, with a parallel plate geometry at temperatures 70, 90, 100, 120, and 140°C. The samples were

1.2 mm thick and 25 mm in diameter. Stress relaxation using 1% step strain was performed at 90°C.

(ii) Transient start-up shear flows and relaxations were studied at 90, 100 and 120°C, and various shear rates, using a modified pressurized multi-speed Mooney viscometer with a grooved biconical rotor of

2.3 cm in radius and the cone angle of 0.2 radian. The samples were preheated for 30 min.

(iii) A capillary rheometer (Monsanto Processabil-ity Tester: MPT) was used at 120°C and different plunger speeds to measure shear viscosity at high shear rates (10° to 103 s-1) in the non-productive system. To employ the Bagley ends correction we used the dies with different length to diameter (L/D) ratios: 5, 10, and 20, but the same die diameter (0.0593 in).

(iv) Transient extension experiments were carried out using a constant strain rate extensional rheometer

1914

of a Meissner type in a water bath at 90°C, with diameter of samples 3 mm and length 10 cm.

Cure Kinetics

Different methods were used to study cure reactions and kinetics:

(i) A curemeter, bi-conical grooved rheometer (Monsanto Rheometer-100) oscillating at a frequency of 100 cycles/min and ±3° arc, with vulcanization temperatures of 140, 160, and 180°C; (ii) Differential Scanning Calorimetry (DSC) with heating rates of 5, 10, 15 and 20°C/min, and (iii) by measuring the gel content, using Soxhlet extraction apparatus. The interpretation of results of(iii) experiments was based on the Flory—Rehner equation modified for oil-extended system. Samples were prepared using the curemeter at 160°C and different cure times.

Chemorheological Experiments

Cure curves for productive SBR samples were obtained using RMS 800 with oscillation mode at 160 and 180°C at 1 rad/s and 1% strain. The storage modulus was monitored with time at given temperature. The same method was used for preparing partially cured samples with controlled degrees of cure at 160°C. The cease in cure reaction was achieved by quick (during ~30 sec) removing samples from the mixture and quenching them using dry ice. Stress relaxation experiments after a step strain of1% were carried out on partially cured samples at 90°C. The relaxation modulus was monitored with time. Frequency

sweep experiments, in the range © = 0.1-10 rad/s were performed on partially cured samples at 90°C and 1% strain. The cure reaction at 90°C was not observed in our laboratory's time scale. It was also shown that the cure kinetics is independent from the oscillating frequency of curemeter.

3. RHEOLOGICAL PROPERTIES OF UNCURED SBR

Constitutive Equations (CE's)

The rheological properties of uncured SBR were modeled using the well-known specification of a set of nonlinear viscoelastic constitutive equations (CE's), whose most detailed thermodynamic derivation, stability analyses and comparisons with experimental data were recently presented in Ref. [2]. These CE's consist of evolution equations for quasi-independent transient (elastic) strain tensors c for each kth relaxation mode and extra-stresses a , with the total stress being the sum a . We present these CE's only for cases of simple shearing and simple elongation, whose predictions are compared below with experimental data. De-

tailed description of component equations for simple flows is given in Ref. [8].

In case of simple shearing, the equations for components ckij are:

20^ + b(c2k,ii + ck,i2 - 1) = 4y0kCk,i2 dt

2 0,

dc

к,12

dt

+ bCk,i2(Ck,ii + Ck,22) = 2y 0 kCk,22 (la)

ькА1ь к,22

= 1 + Ck,i2, Ik = 1 + C,

к,11

+ C

к,22

The shear stress ct12 , the first N1 and the second N2nor-mal stress differences, are presented as:

CT12 = ck,12 ;

k

N1 = XGk(Ik/3)"(CkM - Ck,22) (1b)

k

N2 = XGk(!k/3)K1 - P)(Ck,22 - 1) + P(1 - Ck.l1]

k

Here the standard notations of Cartesian axes in simple shearing have been used, the index k denotes the number of relaxation modes with relaxation time 0 k and modulus Gk, and y is the shear rate. The initial condition for the start up flow is: Cy|t = 8y. Apart from parameters of linear viscoelastic spectrum {0 k, Gk}, equations (1)—(2) contain 3 "nonlinear" parameters: b, n ~ 0.01, and p (0 < p < 1).

In case of simple elongation ck = diag(^k, 'Xk1 ^kV

and the first and second invariants of c are:

=k

Ik 1 = X k + 2X k1 and Ik2 = X-2 + 2X k. In this case the evolution equation for X k and expression for elongation stress a are:

dXk + b(Xk - 1)(Xk + 1)/(6Xk0k) = XkS M dt (2a, b)

a = XGk(Xk - X-1)[(1 - P)(Ik1/3)" + p(Ik2/3)"/Xk]

k

Here s is the elongation rate. The initial condition for start-up flow is: X k|t = 1.

Comparison of Model Calculations with Experimental Data

1. Linear Viscoelastic Behavior

Discrete relaxation spectrum {Gk,0 k} was obtained using computerized Pade—Laplace/collocation procedure detailed in Ref. [9]. Here the part of higher relaxation spectrum was obtained using G"(ro) data and lower one using relaxation data after step strain. In both cases amplitude/step strain was 1%. The discrete

G'(©), G"(©), Pa 1.E+06

1.E+05

1.E+04

1.E+03 10

- A A -A

1 1 1 I I

,-3

10

,-2

10

-1

100

101 102 aaT, rad/s

Fig. 1. Comparison of model calculations (lines) for dynamic moduli G (1) and G" (2) with experimental data (symbols) for uncured gum SBR. RMS 800 data at 1% strain for reduced temperature 90°C.

relaxation spectrum at 90°C is presented in the table below.

Linear discrete relaxation spectrum for SBR compound:

ek (s) 0.022 0.330 1.63 17.0 111 2.220 Gk (kPa) 112 42.3 19.1 13.9 11.4 8.81

The temperature dependence of relaxation times was well described by the WLF plot, with the shift factor aT = -c1( T - T0)/(c2 + T - T0), where T0 = 363 K, c1 = 13.2, c2 = 361.2. Comparisons of spectrum calculations with experimental data for time-temperature superposed plots of dynamic moduli G(®>), G\®>), and stress relaxation modulus G(t) are presented in Figs. 1 and 2, respectfully.

2. Nonlinear Viscoelastic Behavior

The values of nonlinear parameters b = 1, n = 0.02 in CE's (1a, b) and (2a, b) were taken as recommended in Ref. [8], and parameter p = 0.3 by overall fitting the nonlinear data.

The bi-conical instrument did not allow us to obtain reliable data for normal stress differences. Nevertheless, start up and steady shear flow data were successfully described using above CE's (Fig. 3). The extended steady shearing data obtained for gum SBR in both rotational and capillary instruments (in the latter case using the Bagley correction) are also presented in Fig. 4. It should be mentioned that the gum elastomer exhibited severe extrudate distortion in the capillary rheometer at high shear rates. Similar observations were noted in paper [10] with gum SBR 1500 and po-lybutadiene elastomers.

Comparison of start up extensional experimental data with our model calculation

Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.

Показать целиком