Numerical Analysis of a Reactive Extrusion Process. Part II: Simulations and Verifications for the Twin Screw Extrusion.
Polyethylene (PE) grafted with vinylsilane can be crosslinked in the presence of moisture through hydrolysis and further condensation. As a result, its creep, abrasion, heat deformation and chemical resistances are notably enhanced. Other mechanical properties are also improved. Crosslinked PE has been utilized for power cable insulation, hot water pipes, soft foams, and so on (1, 2). It has been manufactured by a direct reaction between vinylsilane and PE melt except for the low-density PE co-polymerized with vinylsilane through a high-pressure process. This kind of polymer reaction is generally performed in a screw extruder in compounding or forming process. Representative manufacturing methods include the Sioplas process (3) of feeding PE. vinylsilane, and peroxide into an extruder for the grafting reaction, further mixing with a catalyst and forming products in another extruder. Another process known is the Monosil process (4) of feeding all materials into one extruder, and reacting and forming simultaneo usly. These methods are distinguished as the "two-step process" and "one-step process," respectively.
Recently, we have built a new process centered on a modular co-rotating twin screw extruder for the silanized PE. It was also designed to be capable of feeding a couple of reactants independently so as to be applicable to the one-step process. Accordingly, the extruder had several functions such as mixing, reaction, metering and forming. In order to design the reaction system, model analyses on the basis of chemical engineering would play an important role. Many studies have been reported in the field of polymerization (5-7). In contrast, very little attention has been paid to processing itself in the field of polymer modification. The author has once carried out a computer simulation for the controlled degradation of polypropylene by extending the flow analysis network (FAN) method (8). However, its utility was not clarified in view of process engineering since the analysis was limited to a couple of screw elements. In this regard, a more practical simulator should be required. We intend to focus on the num erical analysis of our new reactive extrusion process in this study. It will be based on the reaction kinetics and the rheology proposed in the previous paper (9). The simulated results will be compared with the experimental data in discussion.
A high-density polyethylene (Hizex 2200J, Mitsui Petrochemical) and vinyltrimethoxysilane (Silace S210, Chisso) were employed. Di-t-butylperoxide (Perbutyl-D, Nihonyushi) was used as an initiator. Four parts by weight of the initiator was dissolved in one hundred parts by weight of the vinylsilane to prepare a monomer mixture.
Figure 1 shows the reactive extrusion process we built. The self-wiping co-rotating twin screw extruder (TEX44, Japan Steelworks) consists of 12-division cylinder (C1-C12) and two vacuum vent ports on the fourth barrel (C4) and the ninth barrel (C9). A liquid injection nozzle having a check valve is equipped each on the fifth barrel (C5) and the tenth barrel (C10). A sheet-forming die with 200 mm in width and 2 mm in lip clearance is attached to the die head (D). Pressure transducers and thermocouples are installed in every short barrel ([C.sub.A], [C.sub.B] and [C.sub.c]) and D. A twin plunger pump (NP-FX-20, Nihon Seimitsu) was used to feed the monomer mixture into the extruder through the liquid nozzle on C5, with monitoring pressure and flow rate. The screw has been designed in their configurations to specially adapt to this reactive extrusion. Each screw is made up of 33 pieces of flight screw elements and 11 pieces of kneading disc elements as described in Fig. 2. The diameter is [phi] 47 mm and the to tal L/D comes up to 45.5. Other dimensions of all the screw elements are listed in Table 1.
The PE preliminarily dried at 80[degrees]C in hot air was fed into the extruder. Both two vent ports were evacuated below 50 mmHg before feeding the monomer mixture. Confirming the flow rate and the pressure of monomer as constant, and the temperature and the pressure of polymer as stable, a small amount of the extrudate was collected. Grafted PE (g-PE) was immediately quenched to terminate the reaction. The reaction conversion of g-PE was determined by the ICP emission spectro-chemical analysis (9). Table 2 summarizes operating conditions of the experiments.
The FAN method has been widely applied to two-dimensional flow analyses for a variety of screw extruders and dies. Intensive studies on co-rotating twin screw extruders were done by Szydlowski et aL (10, 11) and Chen et al. (12, 13). They calculated the flow only in the screw region or dealt the flow in the intermeshing region by introducing a model called "piston-cylinder." On the other hand. Kim et al. (14) proposed a procedure to unwind a flow field that includes both screw region and intermeshing region, and succeeded in modeling the whole flow field of a non-intermeshing counter-rotating twin screw extruder. In this study, we employ the same technique to develop a two-dimensional analysis field for the intermeshing co-rotating twin screw extruder. Figure 3 illustrates a structural lattice on the cross section of TEX44. Here, the screw radius Z has been given by:
while 0 [less than or equal to] [theta] [less than] [pi]/2s - [[theta].sub.o]
Z = [Z.sub.o]
While [pi]/2S - [[theta].sub.o] [less than or equal to] [theta] [less than] [pi]/S
Z = [Z.sub.o] ([square root] 4[cos.sup.2] [[theta].sub.s] - [sin.sub.2] [[theta].sub.z]) + [cos.sup.2] [[theta].sub.z])
where [[theta].sub.z] = [[theta].sub.o] + (s - 1)[pi]/s + [theta] (1)
s denotes the number of flight tips, which is two for TEX44. By cutting and unwinding the lattice, one can have a geometry field (channel height distribution between the node a-c-e) on Cartesian coordinates. Figure 4 represents that for two typical screw pieces in TEX44; a full-flight screw element and a kneading disc element. In the figures, [x.sub.1], [x.sub.2], and [x.sub.3] indicate the axial direction, the radial direction and the circumferential direction, respectively.
The FAN method requires the following conservation equations:
[nabla] * [rho]v = 0 (2)
- [nabla]P - [nabla]*[tau] = 0 (3)
On the bases of the hydrodynamic lubrication theory, the Reynolds equation in the screw region is:
[partial]/[partial][x.sub.1] [[H.sup.3]/12[[eta].sub.[gamma]]([partial]P/[partial][x.sub.1])] + [partial]/[partial][x.sub.3] [[H.sup.3]/12[[eta].sub.[gamma]]([partial]P/[partial][x.sub.3])] = [partial]/[partial][x.sub.3] (UH/2) (4)
and one in the intermeshing region is:
[partial]/[partial][x.sub.1] [[H.sup.3]/12[[eta].sub.2[gamma]] ([partial]P/[partial][x.sub.1]) + [partial]/[partial][x.sub.3][[H.sup.3]/12[[eta].sub.2[gamma]]([partia l]P/[partial][x.sub.3])] = 0 (5)
where [[eta].sub.[gamma]] means the shear viscosity at the shear rate [gamma], and H means the flow channel height. These differential equations can be solved by iteration method with a generalized Newtonian fluid equation. Pressure fields and flux fields are respectively described on the two-dimensional coordinates in Fig. 5 and Fig. 6 when the Newtonian fluid of isothermal flow is assumed. They are corresponding to the two analysis fields in Fig. 4, at a flow rate Q of 30 kg/h and a screw rotational speed N of 90 rpm. Figure 7 shows characteristic curves (relationship between pressure rise and flow rate) of all the screw elements used in the experiments. They were obtained by calculating pressure fields at the same operating condition. In this Figure, the point where a curve intersects the abscissa is called an "open discharge," while the point on the ordinate is called a "closed discharge."
First we shall concern ourselves with a non-isothermal behavior. The one-dimensional approach was chosen to take into account the heat transfer and viscous dissipation. All the thermal energy sources including the heat of reaction was ignored. In the useful form of the energy equation;
[rho][C.sub.p] DT/Dt = ([nabla] * k[nabla]T) - ([tau]:[nabla]v) (6)
[rho] is the density, [C.sub.p] is the specific heat and k is the thermal conductivity of the PE melt. If a convection coordinate system (replacing t with residence time [t.sub.R]) and an isothermal boundary condition are employed, the thermal equation can be written as follows (15].
[rho][C.sub.p] dT/[dt.sub.R] = 12K([T'.sub.B] - T)/[H.sup.2] + [eta] (1/2 [[pi].sub.[gamma]]) (7)
The first term in the right side represents the heat conduction where [T'.sub.B] is the boundary temperature of polymer fluid. For practical benefits, we replaced the term with one including a heat transfer coefficient h.
[rho][C.sub.p] dT/[dt.sub.R] = -h([T'.sub.B] - T)/H + [eta](1/2 [[pi].sub.[gamma]]) (8)
The second Item is the rheological property of g-PE. According to our previous study, the shear viscosity can be empirically described as a function of temperature and average molecular weight (9):
[[eta].sub.[gamma]] = [[eta].sub.o]/1 + C[([[eta].sub.o][gamma]).sup.0.807]
[[eta].sub.o] = B exp 26070/8.314 (1/T - 1/473.2)
B = 1.056 x [10.sup.-17] [[M.sub.w].sup.3.4] + 523.9
C = 1.114 x [10.sup.-5] [M.sub.z]/[M.sub.w] - 2.645 x [10.sup.-5] (9)
where [M.sub.w] is the weight-average molecular weight and [M.sub.z] is the z-average molecular weight. For simple shear flow, the magnitude of [gamma] equals the square root of the second scalar invariant, that Is defined as:
1.2, [[pi].sub.[gamma]] = [([partial][v.sub.1]/[partial][x.sub.2]).sup.2] + [([partial][v.sub.3]/[partial][x.sub.2]).sup.2] (10)
Reaction kinetics model has also been investigated in the same study. Vanishing speed of Perbutyl-D and reaction speed of this PE and Silace S210 system are given by the equations below.
d[I]/[dt.sub.R] = - [K.sub.d][I]
[K.sub.d] = exp(-160511/RT + 37.68) (11)
dq/[dt.sub.R] = K(1 - q) [square root][I]
K = exp(-39946/RT + 12.61) (12)
In Eq 11, [I] is the concentration of peroxide and [k.sub.d] is its decomposing rate constant. In Eq 12, q is the reaction conversion and K is its apparent rate constant. Both rate constants are described with these Arrhenius formulas.
Another kinetics we need to address is for the molecular weight distribution (MWD) function of g-PE. The following successive equation allows us to predict a change in MWD through this polymer reaction (9).
[[[P.sub.n]].sub.k] = [[lambda].sub.2]/n + ([[[P.sub.n]].sub.k-1] - [[lambda].sub.2]/n)exp(- n[[lambda].sub.1][delta]t)
[[lambda].sub.1] [equivalent] 2f[k.sub.d][I]/[E] (13)
[[lambda].sub.2] [equivalent] [[[sigma].sup.n].sub.r=1] r[[P.sub.r]](n - r)[[P.sub.n-r]]/[E]
where [E] is the concentration of ethylene group and [[P.sub.n]] is the concentration of PE molecules with a degree of polymerization n (the number of monomer units).
Up to this point, we have had a series of basic equations for hydrodynamics, temperature, shear viscosity, reaction conversion and MWD. In what follows, numerical simulation for a reactive extrusion will be explained with reference to the diagram in Fig. 8.
Operating conditions including Q, N and local set (boundary) temperatures [T.sub.Bi] are introduced as well as screw dimensions and configurations. The initial values [[I].sub.o] and [[psi].sub.o] (MWD function of the PE used) are also required. Instead of a whole simulation, a fluid temperature measured at the short barrel [C.sub.A] in each experiment is employed to avoid difficulties in the modeling for solid conveying and melting in the upstream screw.
Die characteristics [delta]P - Q can be written as a formula:
[delta]P = [zeta][eta]Q (14)
where [zeta] is an empirical parameter (= 47.6 X 3600 [kg.sup.-1] for the die used in our experiments). Pressure at the cylinder head [P.sub.i=c] can be estimated when the pressure at the die exit is assumed to be atmospheric (P [congruent] O).
Pressure and Filling Factor Profiles
Calculating [delta][P.sub.i] by each screw element with the FAN method, a local pressure [P.sub.i] along the screw axis will be determined from the top screw (i = c-1) to the root screw (i = 1):
[P.sub.i] = [P.sub.i+1] - [delta][P.sub.i] (15)
while [P.sub.i] [less than] 0, then [P.sub.i] = O.
A local filling factor [[varphi].sub.l] can be defined as the ratio of the flow rate over the open discharge [Q.sub.od] at each screw element:
[[varphi].sub.i]= Q/[Q.sub.[od.sub.i]] (i = c - 1 [sim] 1) (16)
while ([[varphi].sub.i] [greater than] 1, then [[varphi].sub.i] = 1.
Residence Time Profile
Internal residence time [t.sub.[R.sub.i]] from the root screw to the top screw (or between two arbitrary screw elements) will be calculated by summing the time increments [delta][t.sub.[R.sub.i]]:
[t.sub.[R.sub.i]] = [[[sigma].sup.i].sub.i=1] [delta][t.sub.[R.sub.i]]
(i = 1 [sim] c) (17)
[delta][t.sub.[R.sub.i]] = S/Q [[varphi].sub.i] [delta][x.sub.1]
S is the cross section of flow channels (it is constant for TEX44). The time at the die exit equals [t.sub.Ri=c] plus the residence time in the die.
Temperature and Reaction Conversion Profiles
Equation 8 gives the fluid temperatures as a function of [t.sub.R]. A local temperature [T.sub.i] is determined by incorporating with the residence time profile. It can be calculated along the screw axis from the protion in the short barrel [C.sub.A] (i = a - 2) to the top screw (i = c). Simultaneously, Eq 11 and Eq 12 give the reaction conversions as a function of [t.sub.R]. A local conversion [q.sub.t] is determined in the same direction from the monomer injecting portion (i = a) to the second vent portion (i = b). Euler's method may be useful to solve these differential equations, with [rho] = 940 kg/[m.sup.3], [C.sub.p] = 2750 J/(kgK) and h = 350 W/([m.sup.2]K) as all constants.
MWD and Shear Viscosity Profiles
Equation 13 provides a MWD function [psi] of which mean values are given by:
[M.sub.w] = [m.sub.o] [[[sigma].sup.[infinity]].sub.r=1] r[[P.sub.r]] (18)
[M.sub.z] = [m.sub.o] [[[sigma].sup.[infinity]].sub.r=1] [r.sup.2][[P.sub.r]]/[[[sigma].sup.[infinity]].sub.r=1] r[[P.sub.r]]
Finally, a local zero shear viscosity [[eta].sub.oi] is calculated by introducing [M.sub.wi], [M.sub.zi] and [T.sub.i] into Eq 9.
All the procedures are repeated with thus obtained new [[eta].sub.oi] function from the one for the pressure profile. Note that the profiles of pressure and filling factor over the extruder are calculated in the backward direction, i.e., from downstream to upstream, whereas residence time, reaction conversion, MWD and viscosity are calculated in the forward direction from upstream to downstream. Figure 9 explains the flow chart of our computation.
As described in Fig. 2, the screw in the twin screw extruder has been designed to have separate functions including melting, venting, reaction, another venting and pressurizing, in sequence. The reaction zone lies between the two vent zones in the midst of the extruder. At the injection nozzle on C5, the monomer is pressurized over its vapor pressure so as to be liquefied. It is fed into the compressed PE that has already melted. That helps with rapid mixing and prevents direct contact of the monomer to the wall surface in the inner barrel. In addition, the monomer mixture rarely has a chance to leak
outside of the extruder or to be exposed to oxygen that may hinder the radical reaction. We have confirmed not only that the reaction efficiency was enhanced but also that the accumulation of by-products (maybe condensed vinylsilane) on the wall surface was minimized (16).
The contribution of the first vacuum vent on C4 is to remove the moisture that PE originally contains, which causes the condensation polymerization of vinylsilane. Meanwhile, the second vacuum vent on C9 is to remove unreacted monomer that may cause bubble formation in g-PE. It has been found to be effective for a longer life of production, particularly, in a one-step process with introducing crosslinking catalysts (such as dibutyl-tin-dilaurylate) at C10 (17).
Figure 10 shows the simulated result of a reactive extrusion at Q = 20 kg/h, N = 120 rpm and [T.sub.B] = 160[degrees]C. This operating condition is equivalent to that of No. 1 in Table 2. It represents the profiles of pressure, filling factor, temperature, cumulative residence time, reaction conversion and zero shear viscosity. (The simulation for the melting zone (Cl [sim] 03) has been conducted just on the melt flow model.) In the top Figure, fully filled and pressure elevation are observed at the positions where kneading discs or left hand screws have been installed, and near the cylinder head. All the other positions are in starved state. The filling factor varies from position to position, depending on the pressure profile. The average fill factor over the whole screw is approximately 40%. In the middle one, the average residence time is found to be 170 s from Cl to C12, and 90 s in the reaction zone from C5 to C9. On account of viscous dissipation, the fluid temperature gradually increases to 185[degrees]C at the short barrel [C.sub.B], to 192[degrees]C at the [C.sub.c], and to 216[degrees]C at D. In the bottom graph, the reaction conversion rises right after the monomer feeding port on C5, and it reaches almost 80% at the end of reaction zone in C9. The conversion has been left constant after the second vent zone because the concentration of reactants was simply set to be zero at C9. The graph also shows the decrease of zero shear viscosity. It is found that the progress of reaction didn't much influence the fluid viscosity as we expected, but the temperature elevation did.
Figure 11 shows the results in the case of Q = 50 kg/h. The filling factor and the pressure are higher than those of Q = 20 kg/h. Consequently, the residence time has become shorter and the reaction conversion has become lower. Little difference, however, is seen in the profiles of temperature and viscosity. Figure 12 shows the results for N = 150 rpm.
Figure 13 and Fig. 14 compare the calculated results with experimental data. They show the influences of throughput and screw speed on the reaction conversion and average residence time. The conversion goes down as the throughput increases, and this is attributed to the shortened residence time. The screw speed has little effect on the reaction conversion even though the residence time has slightly shortened. All in all, the agreements between simulation and experiment are favorable. The mean residence time (solid triangle) in the Figures was obtained from the residence time distributions in Fig. 15, which had been measured by using a pigment tracer in the experiments No. 1 [sim] 6. Figure 16 is another comparison, but in terms of the set temperature. It turns out that there are deviations in the absolute values, whereas the trend is correct.
So far, the simulation has delivered higher reaction conversion than the experimental data in spite of the shorter residence time. This conflict is attributed to the over-estimation of fluid temperature in the extruder, which is shown in Fig. 17. It indicates the calculated temperature profiles (lines) and the temperatures measured at the short barrels and the die head (plots). This deviation might result in the over-estimation of reaction conversion for a set temperature of 180[degrees]C and below in Fig. 16, and of 160[degrees]C in Figs. 13 and 14. The employment of inappropriate heat transfer coefficient is considered to be the root of this problem. We see another deviation between the experiment and simulation in Fig. 18, which describes the reaction conversion as a function of the composition of monomer mixture. According to our kinetics model, the reaction conversion would not be dependent on the concentration of vinylsilane but only on that of peroxide.
Our newly designed reactive extrusion process for vinylsilane grafted polyethylene was investigated with developing a computer simulation. The basic models were organized for the reaction kinetics and shear viscosity. Flow in the co-rotating twin screw extruder was analyzed by the FAN method on the unwound flow field consists of two screw region and an intermeshing region. The iterative procedure was then devised to calculate the local pressure, filling factor, residence time, temperature, reaction conversion and shear viscosity.
Through the verifications, our simulator was found to be appropriate and available for virtual experiments to some extent. However, several problems on the heat transfer and the dependence of monomer composition were disclosed. Also, considerations to the mixing effect on reaction kinetics have been avoided. We employed the apparent rate constant involving the mixing effect. Indeed, this solution is necessarily incomplete since the constant was not evaluated in an extruder but a batch mixer. We must substantially deal with this in future works.
[C.sub.p] = Specific heat, [Jg.sup.-1] [K.sup.-1].
D = Screq diameter, m.
h = Heat transfer coefficient, [Wm.sup.-2][K.sup.-1].
H = Height of flow channel, m.
i = Local position on screw axis
(i = 1,2, ..., a, ..., b, ..., c-1, c).
k = Thermal conductivity, [Wm.sup.-1] [K.sup.-1].
[k.sub.d] = Rate constant of the peroxide decompostion, [s.sup.-1].
K = Apparent rate constant of the graft reaction, [mol.sup.-0.5][s.sup.-1].
L = Screw length, m.
[M.sub.w] = Weight-average molecular weight. -
[M.sub.z] = Z-average molecular weight, -
N = Screw rotational speed, rpm.
n = Number of monomer units in a polymer molecule, -
P = [Pressure, Pa.
q = Reaction conversion, -
Q = Throughput, kg/h.
r = Number of monomer units in a polymer molecule. -
R = Gas constant, [JK.sup.-1] [mol.sup.-1] (R = 8.314).
s = Number of screw flight tips, -
S = Cross section of flow channel, [m.sup.2].
t = Time, s.
[t.sub.R] = Residence time, S.
T = Temperature, K.
[T.sub.B] = Set temperature, [degrees]C, or Boundary temperature, K([T.sub.B] = [T'.sub.B] - 273.2).
U = Linear screw velocity, [ms.sup.-1].
v = Velocity vector, [ms.sup.-1].
[x.sub.1],[x.sub.2],[x.sub.3] = Coordinates, m.
Z = Screw radius, m.
[gamma] = Shear rate, [s.sup.-1].
[zeta] = Constant in the die characteristic, [kg.sup.-1].
[eta] = Shear viscosity, pa.s.
[[eta].sub.o] = Zero shear viscosity, Pa.s.
[theta] = Angle, rad.
[[lambda].sub.1],[[lambda].sub.2] = Constants in the crosslinking model.
[rho] = Density, g [m.sup.-3].
[tau] = Deviatoric stress tensor.
[varphi] = Filling factor, -
[psi] = Molecular weight distribution function.
[[pi].sub.[gamma]] = Second scalar invariant of the shear rate, [s.sup.-2].
(1.) B. A. Sultan and M. Palmlof, Plastics, Rubber and Composites Processing and Applications, 21, 65 (1994].
(2.) R. L. Silverman, Wire Journal International, January, 68 (1994).
(3.) H. G. Scott, U.S. Patent 3,646,155, Midland Silicones (1972).
(4.) P. Swabrick, U.S. Patent 4,117,195, BICC Ltd. Maillefer (1978).
(5.) K. J. Ganzeveld and L. P. B. M. Janssen, Polym. Eng. Sci, 32, 457 (1992).
(6.) W. Michaeli and A. Grefenstein, Advances in Polymer Technology. 14, 263 (1995).
(7.) H. Kye and J. L. White, Int. Polym. Process, 11, 129 (1996).
(8.) T. Fukuoka and K. Min, Seikei Kakou, 7, 521 (1995).
(9.) T. Fukuoka, Polym. Eng. Sci. Part I, this issue.
(10.) W. Szydlowski, R. Brzoskowski, and J. L. White, Int. Polym. Process, 1, 207 (1987).
(11.) W. Szydlowski and J. L. White, Int. Polym. Process, 2, 142 (1988).
(12.) Z. Chen and J. L. White, Int. Polym. Process, 6, 304 (1991).
(13.) Z. Chen and J. L. White, Polym. Eng. Sci., 34, 229 (1994).
(14.) M. H. Kim, J. L. White, K. Min, and W. Szydlowski, Int. Polym. Process, 9, 87 (1989).
(15.) T. Fukuoka and K. Min, Polym. Eng. Sci., 34, 1033 (1994).
(16.) T. Fukuoka and T. Fukuoka, Japan Patent Application Information. 96-017545 (1992).
(17.) M. Okabe and T. Fukuoka, Japan Patent Application Information, 96-017543 (1992).
Dimension List of the Screw Elements. Length Lead Number Symbol Type (mm) (mm) of Discs FF-1 full-flight (right) 66 66 -- FF-2 [up arrow] 55 55 -- FF-3 [up arrow] 44 44 -- FF-4 [up arrow] 33 33 -- FF-5 [up arrow] 22 44 -- BF-5 full-flight (left) 22 44 -- ND-1 kneading disc (neutral) 44 -- 5 FD-1 kneading disc (right) 44 88 5 BD-1 kneading disc (left) 44 88 5 TR torpedo ring 22 -- -- Common geometry number of flight tips, s : 2 screw diameter, D : 47 mm screw axis distance, [z.sub.i] : 38.5 mm tip clearance : 0.4 mm Operating Conditions for the Experiments. Exp. Throughput Screw Speed Set Temperature Initiator Conc. No. Q (kg/h) N (rpm) [T.sub.B] ([degrees]C) [I] (wt%) 1 22 120 160 0.08 2 31 [up arrow] [up arrow] [up arrow] 3 43 [up arrow] [up arrow] [up arrow] 4 50 [up arrow] [up arrow] [up arrow] 5 22 90 [up arrow] [up arrow] 6 [up arrow] 150 [up arrow] [up arrow] 7 24 120 140 [up arrow] 8 [up arrow] [up arrow] 160 [up arrow] 9 [up arrow] [up arrow] 180 [up arrow] 10 [up arrow] [up arrow] 200 [up arrow] 11 [up arrow] [up arrow] 160 0.04 12 [up arrow] [up arrow] [up arrow] 0.12 13 [up arrow] [up arrow] [up arrow] 0.08 14 [up arrow] [up arrow] [up arrow] [up arrow] 15 [up arrow] [up arrow] [up arrow] [up arrow] Exp. Monomer Conc. 2nd. Vent No. [M] (wt%) (on/off) 1 1.0 on 2 [up arrow] [up arrow] 3 [up arrow] [up arrow] 4 [up arrow] [up arrow] 5 [up arrow] [up arrow] 6 [up arrow] [up arrow] 7 [up arrow] [up arrow] 8 [up arrow] [up arrow] 9 [up arrow] [up arrow] 10 [up arrow] [up arrow] 11 [up arrow] [up arrow] 12 [up arrow] [up arrow] 13 0.7 [up arrow] 14 1.3 [up arrow] 15 1.0 off Common conditions C1[sim]C4 : 170[degrees]C C5[sim]C10 : [T.sub.B] C10[sim]Die : 200[degrees]C [M] : 1 wt%
|Printer friendly Cite/link Email Feedback|
|Publication:||Polymer Engineering and Science|
|Date:||Dec 1, 2000|
|Previous Article:||Numerical Analysis of a Reactive Extrusion Process. Part I: Kinetics Study on Grafting of Vinylsilane to Polyethylene.|
|Next Article:||Biodegradable Polymer Blends of Poly(L-lactic acid) and Gelatinized Starch.|