22 Use of the Arrhenius Equation in Multicomponent Systems N. S. BAER Conservation Center, Institute of Fine Arts, New York University, 1 East 78th Street, New York, N.Y. 10021 N. INDICTOR Chemistry Department, Brooklyn College, City University of New York, Brooklyn, N.Y. 11210
The literature contains a number of examples of the succesful application of the Arrhenius equation to multicomponent systems where the principal component is paper. In these studies, the logarithms of rate constants for physical or chemical properties are plotted vs. 1/T to give straight lines. This approach has been applied to systems as diverse as rosin sized papers and clay filled papers. However, for some systems, physical strength measurements —e.g., folding endurance (TAPPI T-511su-69) and breaking strength (TAPPI T-404ts-66)—demonstrate the independent aging of the components leading to complex, nonlinear Arrhenius plots. Examples from studies of various adhesive-paper model systems are discussed.
Synthetic polymers, often possessing uniquely desirable working proper^ties and physical appearance, are finding ever wider use by artists and conservators. For example, poly (vinyl acetate) emulsions have been used for collages (4,5), the production and conservation of books (6,7), and the conservation of textiles and paintings (8,9). It has become essential to study the behavior of new materials and to evaluate their long-term behavior as individual materials and as components in the complex systems which make up artistic and historic artifacts. Our experience with a wide range of natural and synthetic polymers—e.g., 336
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methylcellulose (10), poly (vinyl acetate) (3, II), poly (vinyl alcohol) (I), soluble nylon (I), glues (2), and starches (10)—as part of paperpolymer systems has demonstrated that the test procedures, well defined for papers, are generally difficult to apply to these more complex systems. In the absence of sample banks of naturally aged materials (12), the need for data on the long-term behavior of such materials suggests the use of accelerated-aging techniques. Any reasonable testing procedure must demonstrate that no new chemical reactions are introduced under the conditions obtained in the test. The appropriate criteria for such procedures are embodied in the Arrhenius equation. Note that the goal of an evaluation program is often the evaluation of a series of related materials and is not necessarily the direct prediction of specific regression times for physical properties. The Arrhenius equation and its use in paper permanence testing is reviewed elsewhere (13) in this monograph. It is, however, important to examine the problems which arise when Arrhenius plots are extended to complex systems. Since concentrations are not measured directly for paper/adhesive systems, rate constants must be obtained from analogs— e.g., folding endurance, tensile strength, brightness, etc. The most useful test measurement for untreated paper has been varying fold endurance with time of aging for elevated temperatures. Unfortunately, with poly mer systems, changing fold strength arises from a multiplicity of mecha nisms—e.g., solvent evaporation, oxidation, degradation, and chemical set—some of which tend to weaken and others to strengthen the system. In the current study of adhesive/paper systems we seek to identify those circumstances appropriate for the application of an Arrhenius equation and to identify those factors which preclude that simple application. Tensile Stress In Figure 1 the generalized behavior of adhesive/paper systems of varying physical properties is illustrated. Elongation and breaking strength under stress are generally relevant measurements for adhesive/ paper systems although the limited elongations obtained for paper have led to a neglect of this significant variable. As shown in Figure 1, one may experience independent rupture of the paper and adhesive or simul taneous breaking, depending on the degree of penetration of the applied polymer into the paper substrate and depending on the brittleness of the polymer. It is important to observe and to record the physical appearance of specimens under tensile stress throughout the measurement rather than merely to record the stress-strain behavior.
338
PRESERVATION OF PAPER A N D TEXTILES
AOHESIVE/
AOHESIVE/ PAPER SYSTEM
PAPER
SYSTEM NO
WITH
PENETRATION
PENETRATION
t
-"WW
BRITTLE ADHESIVE/ FLEXIBLE PAPER
TENSILE
Figure 1.
STRESS
ADHESIVE/ PAPER SYSTEM
ADHESIVE/ PAPER SYSTEM FLEXIBLE ADHES I V E / BRITTLE PAPER
TENSILE
STRESS
Behavior of adhesive-paper systems under tensile stress
Folding Endurance Most frequently, studies of permanence have assumed or implied first-order kinetics for folding endurance measurements on papers which have undergone accelerated aging at elevated temperatures (13-16). The general experimental arrangement for such measurements is presented in Figure 2. It is obvious that the folding endurance measurement is a function of many variables. The increasing stress at the edges as sheet thickness increases has received only limited attention although thickness appears in some proposed equations relating folding endurance to tension
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(17). Also neglected is the role of elongation. As the folding progresses and elongation occurs, new surface is exposed during folding, and in springloaded folding endurance instruments, the tensile strength decreases. This continuous alteration of the system increases in importance for paper/polymer systems where the polymer may undergo significant elongation. It is therefore recommended that elongation for both paper and polymer be recorded and that an instrument with dead weight for tension be used in folding endurance measurements where elongations become appreciable. Though all of the variables in the folding endurance measurement have not been identified, it is clear that abrasion resistance is one of the properties being measured. This combined with the increased stress on the edges complicates the data for composite systems. For a brittle adhesive only partially penetrating a paper substance, the embrittlement of the adhesive may substantially reduce the folding endurance of the system; if such an adhesive is removed mechanically from the substrate, the paper alone suffers little reduction in folding endurance. Similarly, in a study of papers laminated with Ultraphan H K (18), the laminated
FOLDING
ENDURANCE B R I T T L E
FOLDING
ENDURANCE F L E X I B L E
Figure 2.
ADHESIVE
ADHESIVE
FLEXIBLE
PAPER
BRITTLE
PAPER
Folding endurance behavior of adhesive-paper systems
340
PRESERVATION OF P A P E R A N D TEXTILES
system demonstrated reduced folding endurance when compared with the unlaminated paper. This behavior persisted under conditions of accelerated aging. It was noted that the original laminating sheet was 40 p thick and increased the thickness of the paper substrate by 20 to 150-170 fx. The combined effects of penetration and increased thickness led to a system with reduced folding endurance though an examination of the individual components predicted the opposite effect. In the examples presented below, polymer-paper systems are exam ined for cases where there is complete impregnation of the substrate to form what behaves as a single component (poly(vinyl alcohol), soluble nylon, and Regnal); for cases where penetration is limited and the polymer and substrate behave in a generally separate manner (glues); and for cases where a range of behaviors—from apparent interactive to apparent independent—is observed although penetration is limited (poly v i n y l acetates)). Table I.
Designations and Suppliers of Materials
Designation
Supplier
Form Applied
J . T . Baker World Patent Development E . I. DuPont
5% in water" 5% stock solution ' 5% in 90/10 methanol/water
Gane Bros. & Lane S. Schweitzer Gane Bros. & Lane
24%, 35% and 47% in water 34%, 67% in water 36%, 71% in water
Impregnating Agents Poly (vinyl alcohol) U228 Regnal Copolymer Zytel 61 N y l o n d
6
Glues Ganes Flexible Glue 849 Sta-flat Yes Stikflat
Poly (vinyl acetate) Emulsions Airflex 400 Books aver Elmer's Glue A l l Elvace 1874 Everflex A Everflex G Flexbond 800 Jade 403 e
a 6 c d 6
A i r Products Delkote Borden E . I. DuPont W . R . Grace W . R . Grace A i r Products Jade Adhesives
as supplied as sur. applied as; isupplied as supplied as supplied as supplied as supplied as sur applied
A l l solute percentages given by weight. The major solvent component is ethanol. The product is also supplied with a 5 % M g ( C 2 H s 0 2 ) 2 buffer. Currently available as Elvamide 8061. Also available as Daratak A .
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iNDiCTOR
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Experimental Materials and Methods of Application. All paper substrates for the impregnating agent/paper system studies were a buffered wood sulfite, Gracie & Sons Acid-Free Lining Paper, Lot 3 (supplied by Charles R. Gracie & Sons, Inc., New York, N.Y. 10022). Samples were all cut in 0. 5 χ 6-in. strips with the long direction parallel to the machine direction. All paper samples for the poly (vinyl acetate )/paper and glue/paper studies were Whatman chromatography paper #1, basis weight 87 g/m , thickness 0.16 mm, medium flow rate, supplied in 0.5-in. X 300-ft rolls, cut in 6-in. lengths. The materials used to prepare the polymer-paper composite systems are listed in Table I. Complete descriptions including suppliers' comments are provided in earlier studies (1,2,3). The procedure for applying the polymer material to the paper con sisted of brushing the material on a single side of the test paper and permitting solvent evaporation in a controlled atmosphere (23 ± 1°C, 50% r.h.) for 24 hr. A loaded A-in. brush was brought back and forth over the paper sample for a total of five strokes. For measurement of breaking strength and elongation of poly (vinyl acetate ) /paper "sand wiches," two strips of Whatman chromatography paper held together by a layer of adhesive were prepared and aged. The samples were prepared by brushing a A-m. brush loaded with adhesive back and forth over one strip of paper for a total of five strokes. A second strip was imme diately placed on top and pressed lightly. The samples prepared in this manner were placed between 12-in. square Teflon sheets under a 10-lb weight for 3 days. After this period, the samples were equilibrated in an environmentally controlled room (23 ± 1°C, 50% r.h.) for one day and then aged at 95°C for varying periods. Aging of Samples. The treated and untreated samples were placed in ovens at various temperatures (21°C, 50% r.h.; 60°C, 10% r.h.; 80°C, < 10% r.h.; 95°C, < 10% r.h.; and 100°C, < 10% r.h.) for periods of 1, 5, 9, 16, and 50 days. On completion of each aging period, six replicate samples were removed and equilibrated at 23 ± 1°C, 50% r.h. for 72 hr. Folding Endurance Tests. Measurements were performed on a Tinius-Olsen model no. 2 instrument ( also known as a "folding endurance tester" (MIT)) according to ASTM method D-2176-63T on samples cut in the same machine direction. The large standard deviation observed (compared with untreated papers ) reflects nonuniformity in sample thickness produced by the above methods of adhesive application. Generally, it was observed that the treated paper ruptured before the adhesive. The double folds to rupture the paper and the double folds to complete rupture of the system are reported. Breaking Strength and Elongation. The test specimens were then examined under tensile stress on an Instron model T M - M 1101 Universal Tester equipped with 100-kg tension load cell (2-, 5-, 10-, 20-, 50-, 100-kg ranges) and pneumatic grips. The data were recorded as stress vs. time under a uniform increase in extension. The initial jaw separation was 38.1 mm and the initial elongation rate was 0.02 mm/sec. The breaking strength (kg) and elongation (mm) were read from this stress-elonga tion curve. 2
3
3
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PRESERVATION OF P A P E R A N D TEXTILES
Results and Discussion Impregnating Agents. The materials studied, poly (vinyl alcohol), soluble nylon, and Regnal, are described in Table I. All materials impreg nated the paper substrate completely, leading to a system which behaved as a single component in folding endurance tests (Table II). This result was not unexpected since many papers evaluated in paper permanence studies were sized with similar polymeric materials. A way to interpret these data is to attribute the entire deterioration of fold endurance to the polymer. One set of data defies this interpretation—i.e., Regnal to which magnesium acetate was added. There the alkaline reserve of the buffered paper was inadequate to overcome the detrimental effects of the hydrolysis of the magnesium acetate, leading to a reduction in folding endurance to a value below that of the untreated paper aged for a comparable period. Glues. Three glue preparations, Yes, Sta-flat, and Ganes Flexible Glue, are described in Table I. Folding endurance was obtained for samples of paper coated with varying thicknesses of glue and then aged as a system at temperatures of 21°C, 50% r.h.; 60°C, 10% r.h.; 80°C, < 10% r.h.; and 100°C, < 10% r.h. for periods of up to 50 days (Tables III-VI). The Ganes light-coat data are also presented graphically in Figure 3. The heavily coated specimens behaved erratically, suggesting nonuniform sample composition. In general, the paper and adhesive ruptured simultaneously. As expected, the rate of dimunition of folding endurance increased with increasing temperature. At long aging times a marked fold strength weakening was observed whereas at shorter aging times (one and five days) increased strength was usually observed, corresponding to chemical set or solvent evaporation. Such increases in fold strength were most noticeable at lower temperatures. To consider the applicability of the Arrhenius equation, these data were used to produce a plot of the log folding endurance as a function Table II. Double Folds to Rupture" for Artificially Aged ( 1 0 0 ° C , < 10% r.h.) Papers Treated with Impregnating Agents Aging Time Untreated Poly (vinyl alcohol) U228 5% Regnal (unbuffered) 5% Regnal (5% buffer) Zytel 61 Nylon
0 Days
1 Day
5 Days
9 Days
16 Days
13 ± 2 77 ± 14
15 ± 1 66 ± 11
16 ± 3 64 ± 19
17 ± 5 58 ± 15
13 ± 2 35 db 10
67 db 18
72 ± 1 0
48 ± 6
34 ± 10
14 d~ 2
70 ± 17
68 ± 8
32 ± 6
19 ± 4
8± 1
171 ± 23 147 ± 55
142 db 42
° Refers to the paper-adhesive system, 1.5-lb tension.
89 db 22 47 =b 11
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0) 0
L
3.5
UJ
3.0
"D
2.5
343
GANES F L E X I B L E G L U E - H E A T E D AT 60°C
4.0
J V c
Arrhenius Equation in Systems
2.0 1.5 1.0
10
20
4.0
S c
(D
3
T3 C
u
cn
•AYS
30
GANES F L E X I B L E G L U E - H E A T E D AT
3.5
3.0
40
— I
2.5
c
• '3 2 . 0 I
1.0
10
20
DAYS
30
4.0
S
3.5
^
3.0
W
2.5
C (D
TJ C
40
50
GANES F L E X I B L E G L U E - H E A T E D AT 100°C
0) •H
2.0
0 u-
1.5
O)
o
Figure 3.
10
20
DAYS
30
40
50
Log folding endurance vs. time of heating at 60°, 80°, and 100°C for Ganes Flexible Glue
of days of aging to obtain a rate. By omitting the data for 50 days and using the best straight line, Figure 4, the data suggest that the behavior of a glue/paper system can roughly be characterized as first order. This result is not entirely unexpected since glues have a long history as sizing material (19) and in thin surface coats have been considered as a part of papers evaluated for permanence. The difficulties experienced in apply ing Arrhenius plots to thick coats of these materials may be attributed to
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PRESERVATION O F PAPER A N D TEXTILES
Table III.
Double Folds to Rupture
0
for Artificially
Aging Time Adhesive
0 Days
Untreated Yes(L) Yes (H) Sta-flat (L) Sta-flat (H) Ganes (L) Ganes (M) Ganes (H) b
60 ± 180 ± 302 ± 2388 ± 232 ± 4147 ± 5174 ± 3466 ±
1 Day
15 43 137 1624 93 895 1646 1225
60 ± 68 ± 99 ± 318 ± 5± 3243 ± 1455 ± 2096 ±
15 11 45 176 5 1066 564 587
° Refers to the paper-adhesive system, */£-kg tension.
Table IV.
Double Folds to Rupture" for Artificially Aging Time
Adhesive
0 Days
Untreated Yes ( L ) Yes (H) Sta-flat (L) Sta-flat (H) Ganes (L) Ganes (M) Ganes (H) 6
60 ± 180 ± 302 ± 2388 ± 232 ± 4147 ± 5174 ± 3446 ±
1 Day
15 43 137 1624 93 895 1646 1225
58 ± 2 0 52 ± 20 218 ± 120 254 ± 89 80 ± 6 4 3263 ± 643 4414 ± 2499 1763 ± 838
" Refers to the paper-adhesive system, %-kg tension.
Table V . Double Folds to Rupture" for Artificially Aging Time Adhesive Untreated Yes ( L ) Yes (H) Sta-flat (L) Sta-flat (H) Ganes (L) Ganes (M) Ganes (H) b
a
0 Days 60 ± 180 ± 302 ± 2388 ± 232 ± 4147 ± 5174 ± 3446 ±
15 43 137 1624 93 895 1646 1225
Refers to the paper-adhesive system, ^ - k g tension.
1 Day 60 ± 11 44 ± 8 152 ± 15 116 ± 5 5 27 ± 21 4431 ± 1042 6173 ± 1414 2407 ± 1315
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Aged ( 2 1 ° C , 50% r.h.) Papers Treated with Glues Aging Time
6
5 Days
9 Days
60 ± 15 138 ± 4 6 268 ± 136 722 ± 305 85 ± 9 9 706 ± 250 703 ± 199 1474 ± 491
60 ± 15 29 ± 6 74 ± 38 27 ± 1 2 12 ± 1 0 666 ± 248 705 ± 428 914 ± 420
16 Days 60 ± 28 ± 167 ± 18 ± 11 ± 338 ± 187 ± 2565 ±
15 7 175 12 5 188 73 870
50 Days 60 ± 15 28 ± 5 199 ± 103 36 ± 11 36 ± 1 4 232 ± 66 88 ± 32 2131 ± 385
L , M , H denote light, medium, heavy coats, respectively.
Aged ( 6 0 ° C , 10% r.h.) Papers Treated with Glues Aging Time 5 Days 61 ± 160 ± 444 ± 391 ± 129 ± 632 ± 848 ± 3596 ± 6
15 22 96 346 72 196 182 777
9 Days 61 ± 26 ± 260 ± 7 ± 21 ± 584 ± 1412 ± 1911 ±
16 5 126 3 8 252 160 1003
16 Days 51 ± 23 ± 153 ± 4± 54 ± 271 ± 484 ± 1286 ±
6 6 49 3 19 162 176 460
50 Days 60 ± 15 29 ± 7 210 ± 121 4±2 35 ± 3 6 233 ± 99 255 ± 203 1893 ± 476
L , M , H denote light, medium, heavy coats, respectively.
Aged ( 8 0 ° C , < 10% r.h.) Papers Treated with Glues Aging Time 5 Days 70 ± 2 4 132 ± 32 280 ± 55 222 ± 155 23 ± 14 780 ± 217 1037 ± 193 2131 ± 428 6
9 Days 56 ± 17 ± 56 ± 1± 0 265 ± 861 ± 2144 ±
19 5 35 1 122 374 1560
16 Days 57 ± 1 4 13 ± 3 53 ± 49 1± 1 8± 4 107 ± 73 67 ± 51 5587 ± 311
L , M , H denote light, medium, heavy coats, respectively.
50 Days 21 ± 11 ± 17 ± 1± 3 ± 36 ± 212 ± 1711 ±
3 2 9 1 2 33 158 441
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PRESERVATION O F PAPER A N D TEXTILES
Table VI.
Double Folds to Rupture for Artificially 0
Aging Time Adhesive
0 Days
Untreated Yes ( L ) Yes (H) Sta-flat (L) Sta-flat (H) Ganes (L) Ganes (M) Ganes (H)
60 dz 180 ± 302 ± 2388 ± 232 ± 4147 ± 5174 ± 3446 ±
b
1 Day
15 43 137 1624 93 895 1646 1225
55 dz 10 25 ± 7 81 ± 61 17 ± 11 2± 1 1900 ± 832 3533 ± 976 1183 ± 578
° Refers to the paper-adhesive system, ^ - k g tension.
the unevenness in film coating, nonuniform solvent evaporation, and chemical set. The extended data points (50 days) at elevated temperatures all lie above the extrapolated rate line. As the glue deteriorates, the paper may play a greater role in the fold endurance of the system. Poly (vinyl acetate) Emulsions. Table I lists the poly (vinyl acetate) emulsions examined. Folding endurance (Table VII) and break strength and elongation (Table VIII) were measured for coated samples and "sandwiches" of adhesive between two strips of paper substrate before and after aging at 95° C. The wide ranges of folding endurance behavior made Arrhenius plots inappropriate. In two of the systems, Booksaver and Elmers Glue All, the only homopolymers in the group, the paper and adhesive ruptured simultaneously with substantial reduction in fold-
Table VII. Aging Time (Days) 0 1 5 9 16
Double Folds to Rupture for Artificially Aged ( 9 5 ° C , 0
Adhesive Airflex JfiO 817 ± (744 ± 618 ± (600 ± 511 ± (448 ± 376 ± (304 ± 453 ± (409 ±
97 97) 76 76) 45 49) 29 30) 38 36)
Booksaver
Elmer's Glue All
235 ± 25
12 ± 4
9± 1
1
8± 1
2
4± 1
1
3 ± 1
2
Elvace 1874 435 ± 20 (340 ± 40) 768 ± 82 (194 ± 5 8 ) 556 ± 50 (165 ± 28) 592 ± 119 (114 ± 2 4 ) 853 ± 81 (105 ± 16)
° Rupture of the paper-adhesive system. Where the paper ruptured first, result is
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Aged ( 1 0 0 ° C ,
