Idea Transcript
VOLUME 7 NO.l JANUARY 1999
A scientific journal published by Universiti Putra Malaysia Press
Pertanika Journal of Science & Technology About the Journal Pertanika, the poineer journal of UPM, began publication in 1978. Since then, it has established itself as one of the leading multidisciplinary journals in the tropics. In 1992, a decision was made to streamline Pertanika into three journals to meet the need for specialised journals in areas of study aligned with the strengths of the university. These are (i) Pertanika Journal of Tropical Agricultural Science, (ii) Pertanika Journal of Science and Technology (iii) Pertanika Journal of Social Science and Humanities.
Aims and Scope Pertanika Journal of Science and Technology welcomes full papers and short communications in English or Bahasa Melayu in the fields of chemistry, physics, mathematics and statistics, engineering, environmental control and management, ecology and computer science. It is published twice a year in January and July.
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1 EDITORIAL BOARD
| INTERNATIONAL PANEL MEMBERS
Prof. Ir. Abang Abdullah Abang Ali Faculty of Engineering
Prof. DJ. Evans Parallel Algorithms Research Centre
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Pertanika Journal of Science & Technology Volume 7 No. 1, 1999 Contents The Effect of Web Reinforcement on the Shear Capacity of Brick Aggregate Concrete Beams - Md. Monjur Hossain, M. Shamim Z. Bosunia and Md. Hazrat AH
1
Numerical Analysis of Defects Caused by Thermolysis in an Infinite Cylindrical Ceramic Moulding - A.B. Gumel and E.H. Txvizell
13
Multisample Data Acquisition System for Resistance Measurement of High-temperature Superconductors - Ahmad Kamal Yahya, Faizah Md. Salleh and R. Abd-Shukor
25
The Role of the Available Potential Energy in the Atmosphere - Alejandro Livio Camerlengo and Mohd. Nasir Saadon
33
The Relative Growth Rates of the Two-dimensional and Three-dimensional Waves in the Atmosphere - Alejandro Livio Camerlengo and Mohd. Nasir Saadon
39
Sifat Transmisi, Pekali Pupusan dan Keterpantulan Optik Kepingan Poli(metil metakrilat) (PMMA) Didop dengan Metil Merah dan Ferum (III) Asetilasetonat - W.Mahmood Mat Yunus, Mohd Maarof Moksin, Wan Md Zin Wan Yunns, Noraini Abdul Wahab dan Azizah Umam
43
Regime Hydraulic Concepts and Equations: The Case of Klang River, Malaysia - Aziz F. Eloubaidy, T. A. Mohammed, Abdul Halim Ghazali and A. B. Jusoh
57
Dissipation of Hydraulic Energy by Curved Baffle Blocks - Aziz F. Eloubaidy, J.H. Al-Baidhani and Abdul Halim Ghazali
69
ISSN: 0128-7680 © Universiti Putra Malaysia Press
Pertanika J. Sci. & Technol. 7(1): 1 - 1 1 (1999)
The Effect of Web Reinforcement on the Shear Capacity of Brick Aggregate Concrete Beams Md. Monjur Hossain, M. Shamim Z. Bosunia1, Md. Hazrat Ali* Dept. of Civil Engineering BIT Khulna, Bangladesh l
DepL of Civil Engineering BUET Dhaka, Bangladesh
*Dept. of Civil Engineering BIT Chiitagong Bangladesh Received 16 March 1999 ABSTRAK
Kapasiti pancang tiang konkrit campuran batu bata yang diperkukuh tanpa sebarang lapisan dan dengan nisbah pengukuhan lapisan yang berza-beza dikaji dalam penyelidikan ini. Pembiasan pancaran dan retak semasa mengisi muatan direkodkan. Tiang konkrit campuran batu bata dengan pengukuhan lapisan serta dua lapisan kukuh yang diregang didapati menambahkan keretakan yang agak besar. Persamaan keretakan dan tekanan tiang dasar dicadangkan dalam skop kajian ini. Nilai-nilai percubaan kekuatan tiang dasar dibandingkan dengan nilai yang diperoleh melalui persamaan yang dicadangkan oleh ACI dan penyelidikan lain. Persamaan yang dicadangkan di sini mendapati keputusan ujian ini lebih baik daripada yang dibuat oleh para penyelidik lain manakala mengekalkan yang konservatif. Diharap persamaan ini yang dikembangkan di dalam penyelidikan ini akan menyediakan perkara-perkara yang rasional dan asas memulakan konsep yang lazim terdapat dan akan membantu ke arah rumusan kod yang sesuai untuk menyediakan pengukuhan lapisan bagi tiang konkrit campuran batu bata. ABSTRACT
Shear capacity of reinforced brick aggregate concrete beams without any web reinforcement and with varying ratio of web reinforcement was studied in this investigation. Deflections of beams and cracks during the progress of loading were recorded. Brick aggregate concrete beams with web reinforcement and two layers of tensile reinforcement were found to have increased cracking shear stress by a considerable amount. Equations for cracking and ultimate shear stresses were suggested within the scope of this study. The experimental values of ultimate shear strength of beams were compared with the values obtained by equations proposed by ACI and other researchers. The equations proposed herein were found to represent the test results better than those of other researchers while remaining on the conservative side. It is hoped that the equations developed herein will provide a rational and basic point of departure from the prevailing concept and will help towards the formulation of a suitable code to provide web reinforcement for brick aggregate concrete beams. *Corresponding author's address: Ph.D. Student, Faculty of Engineering, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
Md. Monjur Hossain, M. Shamim Z. Bosunia, Md. Hazrat Ali
Keywords: shear capacity, cracking shear stress, brick aggregate, web reinforcement, shear reinforcement parameter INTRODUCTION Brick aggregate plays a key role in the construction field, particularly in countries where sources of natural stone and gravel are limited. For reasons of availability, economy and low weight, this artificial aggregate, of crushed burnt brick, is increasingly becoming popular in the concrete trade. In Bangladesh alone, nearly 90% of concrete construction uses brick aggregate. Crushed brick is also used as aggregate in large quantities in India and Pakistan. Although a thorough study of structural behaviour of concrete made of brick aggregate has been felt to be necessary for a long time, so far only a few studies (Habibullah 1967; Akhtaruzzaman 1968; Rashid 1968; Alee 1976; Akhtaruzzaman 1983; Hossain 1986; Hossain 1984; Shamim-uz-Zaman 1986) have been carried out. But no test has yet been reported for investigating the effect of web reinforcement on the shear capacity of brick aggregate concrete beams. The code provisions followed in Bangladesh are prepared on the basis of studies on conventional stone aggregate concrete in general. These need to be verified for the design of brick aggregate concrete structures. Keeping the above objective in view, the present research was undertaken to investigate the shear problem in particular. Shear failure of rectangular brick aggregate concrete beams with web reinforcement was studied. Concrete strength and web reinforcement are taken as principal variables. MATERIALS AND METHODS Eighteen single span simply supported beams were tested under two-point loading. The load was applied by a 200-ton universal testing machine. A fixed value of shear span ratio equal to 2.5 was maintained for each test. Manually crushed first class brick chips 3/4 inch down grade, and locally available coarse sand, known as Sylhet sand were used as coarse and fine aggregate respectively. Physical properties of the aggregates are given in Table la. TABLE l(a) Physical properties of aggregates Property Fineness modulus Unit weight (lb/cft) (Dry, loose) Unit weight (lb/cft) (dry, compacted) Absorption j (% dry weight) Bulk specific gravity (SSD)
Brick aggregate
Fine aggregate
6.88 60.00
2.65 91.25
64.00
101.87
14.75
1.46
2.00
2.70
PertanikaJ. Sci. & Technol. Vol. 7 No. 1, 1999
Effect of Web Reinforcement on Shear Capacity of Brick Aggregate Concrete Beams
Details of mix proportioning is given in Table l(b). Type 1 normal Portland cement was used. Three grades of concrete with 28 day's nominal strengths of 13.8 Mpa (2,000) psi, 20.7 Mpa (3,000 psi) and 27.6 Mpa (4,000 psi) were selected for this investigation. Average concrete strengths for each beam with details of main reinforcement and shear reinforcement are given in Table 2. TABLE l(a) Details of concrete mix proportioning ratio Nominal strength in psi
2000 3000 4000
Ratio of mix proportion by weight, aggregatesi in SSD condition
Water cement ratio by
Per cubic yard of concrete cement
(lb)
wt
1:2.35:4.46 1:1.90:3.80 1:1.67:3.33
0.75 0.65 0.58
lbs/cu yd = 0.593 kg/m 3 ,
Loose dry state
Sand (lb)1
Aggregate (lb)
911 896 884
1822 1792 1763
406 472 530
1 cubic yard =0.765 m*
TABLE 2 Physical properties of beams Beam designation
Cylinder strength (psi)
25C, 27C2 29C, 32C4 33Q. 36C0
2218 2297 2772 2851 2693 2059
1A,
13A(1
3433 3644 3406 3248 3644 4040 3287
14B, 15B2 16BS 19B4 20B5
4515 4357 4040 4832 4436
3A, 6A,
7A4 10A. 12A,
Average Bottom reinforcement, f & steel ratio
Top
Web
>/; =
reinforcement, f & steel ratio
reinforce ment & (inches)
Aufy sb
0.00 @ 13.!3 44.43 @ 3.0 200.00 @ 4.0 371.20 @ 3.0 495.00 Nil 0.00 NIL
2566
4*8
2*7
/ - 52473 psi As = 2.956 iir p = 0.0547
/ = 46916 psi A\= 1.108 in* p'5= 0.02
4#8
2#7 / - 46916 psi A\ = 1.108 in2 p'%= 0.02
#2 #2 #3 #3
Nil
3569
/ = 52473 psi At = 2.956 in2 pS= 0.0547
#2 #2 #3 #3 #4
@ 13.5 @ 3.0 @ 4.0 @ 3.0 @ 3.5
Nil
0.00 @ 13.5 44.43 133.30 @ 4.5 @ 4.5 412.50 @ 4.0 464.00
Nil
4436
4#8
2#7
/ = 34632 psi
fy = 39362 psi A\ = 1.087 in2 p1 = 0.02
ks = 2.54 in2 p = 0.0525
PertanikaJ. Sci. & Technol. Vol. 7 No. 1, 1999
#2 #2 #3 #3
0.00 45.00 201.00 305.00 407.00 740.00 0.00
Md. Monjur Hossain, M. Shamim Z. Bosunia, Md. Hazrat Ali
TEST RESULTS AND DISCUSSION
The general behaviour of the test beams under load was in good agreement with other investigators (Clark 1951; Bresler and Scordelis 1963; Habibullah 1967; Akhtaruzzaman 1968; Haddadin et al 1971; Hossain 1984;). Typical flexural cracks appeared first in the pure bending zone, followed by flexural and/or diagonal tension cracks in the shear span at increased loading. Diagonal tension cracks generally occur in the middle third of the overall depth, extending upward and downward. Various test data, including the initial flexural cracking load Pf initial diagonal tension cracking load P, failure load Pn and the observed mid-span deflection y are shown in Table 3. This table also includes the mode of failure and ratio of P/Pu, P/Pu and Pf/Pc for each beam. Table 3 reveals that flexural cracks started on an average at 44, 26 and 24% of the ultimate load for 2000, 3000 and 4000 psi series, respectively. Akhtaruzzaman (1968) recorded this value as 24% while Bresler and Scordelis (1963) and Clark (1951) obtained this value as 15 and 20%, respectively. Studies carried out by Clark (1951) and Bresler and Scordelis (1963) were with conventional concrete. The higher TABLE 3 Observed values from beam tests Series
Beam Glexural Diagonal ritimate desig- cracking tension load, Pu nation load, Pf cracking (kip) load, Pc (kip)
Ratio Pf/Pu
Ratio Ratio Pc/Pu Pf/pc
Recorded midspan deflection
Mode of
failure
(kip)
psi
40.0 45.0 55.5 60.0 60.0 41.0
0.44 0.60 0.36 0.50 0.33 0.39
0.50 0.60 0.51 0.50 0.50 0.39
0.87 1.00 0.70 1.00 0.67 1.00
0.09 0.14 0.13 0.08 0.15 0.08
0.25 0.33 0.35 0.40 0.34
33C 36C0
Ki.O
20.0 27.0 28.5 30.0 30.0 16.0
1A, 3A,
15.0 15.0 17.0 14.0 15.0 15.0 15.0
24.0 30.0 25.0 25.0 30.0 30.0 28.0
35.0 56.0 70.0 80.0 86.0 100.0 43.0
0.43 0.27 0.24 0.18 0.17 0.15 0.35
0.68 0.53 0.36 0.31 0.35 0.30 0.65
0.63 0.50 0.68 0.56 0.50 0.50 0.54
0.17 0.12 0.10 0.10 0.15 0.16 0.13
0.27 0.38 0.41
13.0 13.8 15.6 20.0 20.0
30.0 34.0 35.0 30.0 36.0
44.4 64.5 70.0 83.0 80.0
0.29 0.21 0.22 0.24 0.25
0.67 0.53 0.50 0.36 0.45
0.43 0.41 0.44 0.67 0.55
0.18 0.20 0.16 0.15 0.27
0.35
39C, 32C4
3000 psi
10A' 12A;
ISA, 14B,
4000 . 15B9 psi
ym
17.5 27.0 20.0 30.0 20.0
25C, 27C, 2000
yt
16B",/ 19B4 20B.
PertanikaJ. Sci. & Technol. Vol. 7 No. L, 1999
-
—
0.15 0.55 -
_
0.65 0.65
DT DT DT DT DT ST DT DT DT SC SC SC ST DT DT SC F F
Effect of Web Reinforcement on Shear Capacity of Brick Aggregate Concrete Beams
PJPU value recorded in this investigation was due to higher tensile capacity of brick aggregate concrete. Previous authors (Akhtaruzzaman 1983; Hossain, 1984; Shamim-uz-Zaman 1986) also observed higher tensile capacity of brick aggregate concrete. Table 3 also reveals that the critical diagonal tension crack in general appeared at about 42% of the ultimate load, indicating significant reserve strength for brick aggregate concrete beam. It is a common practice to provide stirrup in beams. The ACI provision also advocates providing minimum stirrup. In the presence of stirrup the dowel shear in the main reinforcement becomes more significant. Again, the compactness of the concrete due to shear reinforcement couples with the dowel shear to increase the cracking shear stress. The ratio of cracking shear stress obtained from test to the cracking shear stress calculated by ACI provision (vj/v, ACI) is recorded as high as 1.52 by Haddadin et al (1971) and 1.44 by Bresler and Scordelis (1963), also pointed out that the shear rigidity of the multilayered tensile reinforcement contributes a significant portion of the calculated reserve shear strength due to so-called dowel action. Due to the facts mentioned above and since the brick aggregate concrete possesses higher tensile strength, the analysis of cracking shear stress is justified. In Fig. 1 the ratio of vc/^f' is drawn in ordinate against \rfy/'yjf')\ —"
m
abscissa, where Vr is the cracking shear stress; Vis the maximum shear; M is the maximum moment and ff is the shear reinforcement parameter in which V is ratio of web reinforcement (=AJb$), The results of the beams tested by Haddadin et al. (1971) are higher than corresponding values proposed by ACI. The results of the beams tested in the present study are also well above the corresponding ACI values and can be distinguished by the lower ceiling line shown in the figure. This line is represented by Eq. (1). Since all the points are above this reference line, Eq. (1) may be taken as a safe basis to predict v^ for brick aggregate concrete beams with web reinforcement and multilayered Test Vain*- AC! Group ^
4
l
4
)(
)
(18)
= C(t) + (I - X- 1A2 + X12A2 + &15AS)
It is easy to show that the order of (18) is 0(h2 + I4) as h, 1 -> Oand that, when q = 0, the method is L-stable. To achieve parallel implementation, (18) must first be written in the form = (I - 1A +/ 2 12A2 - /61SA3 + X 4 l 4 A 4 )'c(t) - ]A +X, 12A2 - %1SA3 + X 4 l 4 A 4 )'(l - X 1A - X following which partial-fraction decomposition of the (4, 0) Pade approximant to exp (1A) itself and of the matrix rational expression (the coefficient of lq) in (19) gives C(t+1) = I fsj(I - bjlA)"1C(t) + kj(I - b j l A ^ l q l
(20)
in which bi = b 2 = 0.42626656502702 3 10"1 + i 0.39463295317211, b 3 = B 4 = 0.45737334349730 + i 0.23510048799854, s. = s, = -0.12116960248677 - i 0.20306415938099, 1
2
s3 = s4 = 0.62116960248677 - i 0.59941529409522, io- 2
k( = k2 - -0.51650550237725 3 10* - i 0.86559461699437 3 k3 = H4 = 0.28410641796826 - i 0.27415657720375. Closed-form expressions for the complex constants b., s., k. (j = 1, 2, 3, 4) are not available.
18
PertanikaJ. Sci. & Technol. Vol. 7 No. 1, 1999
Numerical Analysis of Defects Caused by Thermolysis
The solution vector c(t + 1) may then be comuted using the parallel algorithm Processor 1:
(I - r, 1A)W, = s,( (I - r, 1A)W, = k, lq;
Processor 2.
(I - r" 1A) W.( = s3C(t) (I - r31A)W4 = kSC(t)
Then:
C(t + 1) = 2[Re(W,) + Re(W2) + Re(W,) + Re(W4)] r
,t: = t+ 1
in which both coefficient matrices are tridiagonal. The once-only decompositions of the tridiagonal matrices I - rt 1A and I - r31A are carried out by processors 1 and 2, respectively. Each processor employs a tridiagonal solver based on LU-decomposition employing forward and backward substitution, to compute the intermediate vector W. (j = 1,2,3,4) at every time step. This parallel algorithm is to be preferred to the sequential algorithm based on (18) which requires higher powers of the matrix A, because the increased band-width of the coefficient matrix I - 1A +% 12A2 - %1*A3 + X414A4 increases computing costs and storage requirements. An alternative 0(h2 + I4) method which uses real arithmetic and four processors, and is also L-stable, was developed by Voss and Khaliq (1996) and could be adapted for solving (1) (4). Arguably the best-known, single-processor method which could be adapted for solving (l)-(4) is the Crank-Nicolson method (Crank and Nicolson 1947). Unfortunately, this method is only 0(h2 + I2) accurate as h, 1—>0 and is only A-stable, whereas the method given by (18) is L-stable. Lawson and Morris (1978) gave an excellent description of the short-comings of the CrankNicolson method when used to solve problems which have a discontinuity between the boundary condition (3) and the initial condition (4). Lambert (1991), for instance, lists the properties of approximations to exp( 1A) in (16) which lead to A-stable or L-stable methods. The problem solved in the present paper given by (l)-(4) is one-dimensional because of symmetry. Manufactured, ceramic artefacts usually have some symmetric properties which should always be exploited in making calculations. There will be occasions, however, when there will be a need to retain more than one space variable and in solving such problems parallelism in space should be taken into account. Lawson and Morris (1978) and Swayne (1987, 1988) developed single-processor algorithms for solving multi-dimensional PDEs while Twizell et al. (1996) and Taj and Twizell (1997) have developed multi-processor techniques for solving them.
PertanikaJ. Sci. & Technol. Vol. 7 No. 1, 1999
19
A.B. Gumel and E.H. Twizell
BOILING CRITERION: NUMERICAL RESULTS The vapour pressure at the base time level tn is given by
P;1 = exp[-AH v /(RT n ) + a]
(21)
(Evans et ai 1991), in which Tn is the temperature at time tn, and this is updated at time tn+1 by the relation (22) Where
vm = c p pr7[c p vr + 1 + (i - cp)v2n
(23)
in which V"+1 = 0.001098[l + 0.0009774 {(n + 1 ) 1 + 100}]
(24)
V2n+1 - 0.0009595fl + 0.0004985 {(n + 1)1+ 49}]
(25)
and (26)
C p - Co (Matar et al 1993).
A bubble forms when the vapour pressure exceeds the atmospheric pressure. A plot of vapour pressure against temperature computed using the procedure described above with the data given in Table 1 is depicted in Fig 1. Unfortunately, no closed-form solution of the problem (9, 1-4) is available against which the TABLE 1 Parameter values used for computation Parameter
value
Uit
a 1 B D E
22.255 0.5 0.005 0.000692 222000 38940 1.67 3 1016 99 8.3143 0.5 1075 0.361
Pa
AHv M R V
20
s m
mV 1 J mol"1 J mol"1 s"1 J moHKr1 dimensionless kg m"3 dimensionless
Pertanika J. Sci. & Technol. Vol. 7 No. 1, 1999
Numerical Analysis of Defects Caused by Thermolysis Nomenclature Description
Parameter
a >, k., s. b],k| §j c g h
i 1 q(, q r t A B C C* D E H AHv I Kp M Pv Q R T V. Vm Vj V2 W Z p X £1 dQ 0 T
constant constants in partial-fraction decmposition (j=l,2,3,4) complex conjugates of b., k., s. (j = 1,2,3,4) concentration of monomer, c = c(r,t) vector of order M, g = [C*, ..., C*]T increment in r
Units Pa
kgnrs m
i = W-l increment in t vectors of order M, qt = q = [ Q , , . . . , Q i ] space co-ordinate of point on radius of cylinder (0< r < B) time square matrix of order M radius of cylinder numerical approximation to c initial value of c diffusion coefficient activation energy for thermal degradation mass fraction of polymer remaining enthalpy of vaporization identity matrix of order M frequency factor for thermal degradation N o . discretization points in 0 < r < B vapour pressure of m o n o m e r over the p u r e liquid production rate of m o n o m e r caused by pyrolysis gas constant temperature volume fraction of ceramic in ceramic-polymer body volume fraction of m o n o m e r in polymer specific volume of m o n o m e r specific b o l u m e of m o n o m e r intermediate vecotrs (j = 1,2,3,4) heating rate density of polymer interaction parameter for monomer-polymer system region in (r,t) plane b o u n d a r y of Q zero vector of o r d e r M transpose of a vector
PertanikaJ. Sci. & Technol. Vol. 7 No. 1, 1999
m
kg kg
J mol"1 0 < H 650nm). Seterusnya pertambahan kepekatan metil merah kepada 3.1 3 103 mmol/g, 4.7 3 10" 3 mmol/g dan 6.3 3 lO^mmol/g tidak mengubah nilai transmisi optik maksimum PMMA-MM. Pada ketiga-tiga kepekatan tersebut transmisi optik maksimum sampel adalah sama dengan transmisi optik maksimum PMMA tulen, iaitu -91% (lihat Rajah 2). Plot kecil dalam Rajah 2 pada penjuru sebelah kanan bawah menjelaskan perubahan peratus transmisi optik sebagai fungsi kepada kepekatan metil merah yang didopkan kepada PMMA dan dinilaikan pada jarak gelombang 550nm. Transmisi optik yang agak berlainan dengan PMMA-MM ditunjukkan oleh sampel PMMA-FM. Pada sampel Bl pada Rajah 3 misalnya, dimana kepekatan ferum (III) asiitilasetonat dalam PMMA ialah 6.1 3 10"3 mmol/g (4 kali ganda kepekatan sampel Al), lengkung transmisi optik menunjukkan wujudnya satu lengkok minimum pada jarak gelombang 435nm dengan nilai transmisi optik ~ 15% dan nilai transmisi optik maksimum direkodkan pada X=745nm sama dengan transmisi optik PMMA tulen. Dengan menambah kepekatan ferum (III) asitilasetonat kepada PMMA, nilai lengkok transmisi minimum mengecil dan transmisi optik maksimum berkurangan. Untuk sampel B3 (12.3 3 10** mmol/g)
PertanikaJ. Sci. 8c Technol. Vol. 7 No. 1, 1999
49
W.Mahmood, Mohd Maarot Moksin, W. Md Zin Wan Yunus dan Noraini dan Azizah Umam
misalnya, lengkok minimum direkodkan sebagai 5% dengan transimisi maksimum menjadi 78% pada >,=745nm. Merujuk kepada pengecilan peratus transmisi pada X=435nm terhadap pertambahan kepekatan ferum (III) asetilasetonat dalam PMMA ini, satu pengukuran transmisi dilakukan kepada sampel B4 yang didopkan dengan kepekatan yang lebih tinggi iaitu 30.7 3 10"5 mmol/g. Hasil pengukuran sampel B4 menunjukkan bahawa frekuensi penggal transmisi berlaku pada 475nm, iaitu berganjak sebanyak 175nm ke jarak gelombang yang lebih panjang. Pada nilai kepekatan ini juga nilai transmisi optik maksimum bertambah semula kepada 88% pada X = 725 nm. Plot kecil dalam Rajah 3 di sudut sebelah kanan bawah menunjukkan perubahan peratus transmisi optik berubah dengan kepekatan ferum (III) asetilasetonat dalam PMMAyang direkodkan pada X =500 nm. Dalam kes ini peratus transmisi optik mengecil secara tidak linear dengan pertambahan kepekatan ferum (III) asitilasetonat (b) Pekali Pupusan Optik, k Nilai pekali pupusan optik, k untuk semua sampel yang dikaji ditentukan dengan menggunakan kedua-dua kaitan persamaan (3,4) dan (7,8). Rajah 4 menunjukkan nilai k yang diperolehi untuk sampel PMMA-MM dimana nilai k didapati berkurangan dengan cepat dengan pertambahan jarak gelombang pada sela (540-600)nm. Pada ^>600nm nilai k hampir malar terhadap pertambahan jarak gelombang (lihat Rajah 6). Plot nilai k sebagai fungsi kepada jarak gelombang (475-700) nm untuk PMMA-FM ditunjukkan pada Rajah 5. Kedua-dua hasil (Rajah 4 dan 5) tersebut menunjukkan bentuk 0.8
0.6
O 0.4
I |
0.2
0.0 500 i
600
650
700
Jarak gelombang (nm)
Rajah 4. Plot perubahan pekali pupusan optik, k terhadap jarak gelombang untuk sampel PMMA-MM 50
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pengurangan nilai k terhadap jarak gelombang yang serupa. Pada sampel PMMA-FM nilai, k berkurangan dengan jarak gelombang secara mendadak pada sela jarak gelombang (475-600) nm dan untuk A>620nm k berubah dengan lebih mendatar (lihat Rajah 7). Kedua-dua plot kecil dalam Rajah 4 dan 5 dipenjuru kanan-atas masing-masing menunjukkan pertambahan nilai pekali pupusan optik, k terhadap kepekatan pewarna untuk nilai jarak gelombang X = 550nm dan X =500nm. Nilai k untuk semua sampel ditentukan dengan menggunakan kaitan (3, 4) ditunjukkan pada Rajah 6 dan 7 oleh garis yang bersambung sebagai perbandingan dengan nilai k yang dikira dengan menggunakan formula (7, 8). Dapat diperhatikan bahawa kesemua nilai k yang diperoleh dengan menggunakan formula (3, 4) kecuali sampel Al adalah lebih besar dari nilai k diperoleh dari kaitan (7, 8) terutama pada A, > 600nm. Ini menjelaskan bahawa nilai keterpantulan optik pada permukaan sampel dalam kajian ini tidak boleh diabaikan untuk menentukan nilai k yang sebenar bahan dielektrik. Oleh itu, penggunaan persamaan (7) untuk menentukan nilai, k, kepingan dielektrik adalah wajar (Nemoto, 1994). (c) Peratus Keterpantulan Optik dan indeks biasan Keempat-empat sampel PMMA-MM memberikan bentuk keterpantulan optik yang sama . Nilai keterpantulan optik berada antara 3.8-6.4% untuk julat jarak gelombang 470- 800nm. Nilai keterpantulan maksimum 6.4% diberikan oleh Al pada X =600nm dan 700nm dan nilai keterpantulan minimum 3.8% diberikan Pertanika J. Sci. 8c Technol. Vol. 7 No. 1, 1999
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oleh Sampel A3 dan A4 pada X = 470nm. Hasil yang serupa diperolehi untuk sampel PMMA-FM dengan nilai keterpantulan optik berada antara 4.3-6.8%. Rajah 8 dan 9 menunjukkan plot keterpantulan optik pada sudut tuju 45° untuk sampel PMMA-MM dan PMMA-FM. Indeks biasan, n sampel PMMA-MM dan PMMA-FM yang dikaji ditentukan dengan kaedah penentuan sudut Brewster, GB dimana n dikira sebagai n • tan 0B. Rajah 10 menunjukkan contoh plot keterpantulan optik sebagai fungsi kepada sudut tuju untuk sample Al. Indeks 52
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