CONSISTENCY OF RHEOLOGICAL EXPERIMENTS FOR PSA CHARACTERIZATION Dr. Laura Yao, Senior Research Chemist, Scapa North America, Windsor, CT Robert Braiewa, Research Chemist, Scapa North America, Windsor, CT Abstract Rheology has become a common tool in the qualification and development of pressure sensitive adhesives and adhesive products. Researchers use rheology to characterize the physical properties of adhesives and correlate rheological data to conventional adhesive performance properties such as peel, shear, and tack. However, different research groups in the industry may use varying test methods. Each rheological experiment has limitations, and its results are influenced by the test method used. This paper examines the accuracy and precision of rheological experiments through case study. It allows us to develop a better understanding of the reliability of rheology data and the influence of test parameters on the rheological response of different types of pressure sensitive adhesives. Introduction Rheology can be described as the study of the flow of materials when subjected to stress. Purely solid, elastic materials obey Hooke’s law where shear stress is directly proportional to shear strain. This proportion constant is commonly referred to as modulus or elastic modulus. Alternatively, for pure viscous liquids which obey Newton’s law shear stress is proportional to shear rate, and the proportion constant that relates the two is commonly referred to as viscosity. Most polymeric materials, including adhesives, exhibit a combination of these two responses to stress and are classified as viscoelastic. Their deformation can be described by two mechanisms: elastic deformation and viscous flow. The elastic properties are characterized by the elastic modulus, or storage modulus, G', which measures the energy stored by the material. In contrast, viscous properties are characterized by the viscous modulus, or loss modulus, G'', which measures the energy dissipation from viscous flow. The ratio of loss modulus to shear modulus, commonly referred to as tan δ, is another important rheological parameter that relates the relative solid- or liquid-like behavior of a material. The use of both stress and strain control rheometers is becoming more widespread to characterize adhesive performance. Oscillatory experiments such as temperature sweeps and frequency sweeps are popular tests that can be used to evaluate numerous adhesive performance characteristics. For instance, temperature sweeps give valuable information such as Tg and G' over a temperature range, which can be in turn correlated to traditional adhesive properties such as peel adhesion and tack. Frequency sweeps can be used to understand time dependent properties such as die-cuttability and damping performance. The principle of time-temperature superposition (TTS) is useful in extending the frequency range beyond that of the instrument. TTS states that for small stresses and strains, time and temperature can be treated as the same variable. The principle is implemented by running frequency sweeps at different temperatures, then shifting the curves horizontally along the frequency axis until they overlay with a fixed curve generated at a reference temperature. The resultant curve, with extended frequency range, is commonly referred to as a master curve. While these tests are commonly used to compare adhesive formulae for various applications, there is no standardized set of test conditions in the industry, and various research groups may use different

conditions to evaluate materials. It is important to understand the effect of test parameters on the data generated so that comparisons of data from disparate sources are not misinterpreted. It is also important to know the precision of the instrument so that differences in data can be attributed to changes in the adhesive formula or experimental error. Finally, it is useful to understand the limitations of the instrument so that experiments can be designed to maximize its capabilities. This paper addresses the concerns of consistency in rheological experiments. Materials Three solvent-based, pure (non-tackified) acrylic pressure sensitive adhesives “A”, “B”, and “C” were selected for this study. All three adhesives were self-crosslinking through metal chelating chemistry. Adhesive “A” is a general purpose adhesive, with moderate Tg (~ -12°C). Adhesive “B” is a soft, lower Tg (~ -33°C) adhesive. Adhesive “C”, on the other hand, is a firmer, higher Tg (~ -7°C) adhesive. Experiments Sample Preparation Rheology samples were prepared by laminating multiple layers of 5 mil dry adhesive film to a nominal 40 mil thickness. The samples were die-cut to 8 mm diameter discs for rheology experiments. Rheology Experiments All rheology experiments were performed on a TA Instruments AR2000 stress control rheometer (TA Instruments; Newark, DE) using Rheology Advantage Instrument Control V5.2.0 and Rheology Advantage Data Analysis V5.2.18 software. Temperature sweep and frequency sweep experiments were conducted. Temperature Sweep Adhesive samples were loaded between two 8 mm stainless steel parallel plates. The gap between the plates was set and controlled using instrument normal force control. Temperature sweeps were performed from -60 to 200ºC at ramp rates of 3ºC/min and 5ºC/min, and at two different frequencies, 6.28 rad/s and 10 rad/s. The percentage strain was controlled at 0.05%. When operating the instrument in controlled strain mode, data can be generated using either non-iterative or precision sampling modes. Both sampling modes were used in this study and their effects on instrument/data sensitivity will be discussed in the results and discussion section. When non-iterative sampling mode was used, a stress sweep at the experiment starting temperature was performed prior to the temperature sweep. The stress that generated 0.05% strain was used as the initial stress used. Data was collected at 5, 10, 20 and 30 second intervals. Tg and G' at 25ºC [G'(25°C)] were recorded and used to evaluate the consistency of the experiment. Frequency Sweep Adhesive samples were loaded between two 8 mm stainless steel parallel plates. The gap between the plates was set and controlled by instrument normal force control. Frequency sweeps were performed at 0ºC, 25ºC, and 50ºC, over a range of 0.01 to 200 rad/s. G' was recorded at 0.01, 0.1, 1, 10, and 100 rad/s and used to evaluate the consistency of the experiment.

Results and Discussion The following results and discussion are limited to TA Instruments AR2000 rheometer. Temperature Sweep Instrument Precision One of the key physical properties of pressure sensitive adhesives is the glass transition temperature (Tg). It is measured by the peak of tan δ from temperature sweep experiments. Of great interest is the precision and consistency of the experiment. This allows one to identify what range of Tg variation truly results from adhesive formulation and what range of variation can be attributed to instrument sensitivity and instrument and experimental errors. Both data collection mode and data acquisition rate affect the precision of the instrument. The instrument control software, Rheology Advantage Instrument Control V5.2.0, allows data to be collected in non-iterative and precision mode when strain is controlled. The precision mode controls strain by an iterative method, using up to ten cycles to reach the controlled strain. Each iteration takes some amount of time, during which temperature continues to ramp. For this reason, when measuring a rapid transition such as the glass transition region, data points can be spaced at wider temperature intervals. In non-iterative mode, the software uses the previous stress value to predict the new value required to obtain the target strain. This mode is suggested to make rapid measurements rather than to accurately control the strain. Data acquisition rate affects the precision of an experiment by the density of the data, or in other words, the number of data points collected over a specified temperature range. Figure 1 shows the temperature sweep of adhesive “A” using both non-iterative and precision sampling mode at 5, 10, 20 and 30 s/data point. The data point density varies through the temperature range when precision sampling is used, especially for 5, 10, and 20 s/data point acquisition rates. In precision sampling mode, the data points are spaced at wider temperature intervals around the glass transition temperature than they are at higher temperatures. This is because, as described above, when precision sampling mode is applied, the instrument attempts to accurately control strain. When the rapid glass transition takes place, the instrument goes through multiple iterations of different stress values as it attempt to reach the controlled strain. If the iteration process can not keep up with the data collection rate, some data points will be missing, resulting in a wider temperature interval. Table 1 lists the measured temperature interval from the experiment and the temperature interval (ΔTcalculated) calculated from data collection rate and temperature ramp rate for both precision and non-iterative sampling rate. In this experiment, a ramp rate of 5ºC/min was used. ΔTcalculated can be calculated from the following equation, where r is the data acquisition rate in seconds.

rTcalculated ×=Δ605

(a)

(b)

-100.0 -50.0 0 50.0 100.0 150.0 200.0 250.0temperature (°C)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G' (

Pa)

0

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

tan(delta)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G'' (

Pa)

"A", non-iterative, 5s/data"A", precision, 5s/data

-100.0 -50.0 0 50.0 100.0 150.0 200.0temperature (°C)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G' (

Pa)

0

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

tan(delta)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G'' (

Pa)

"A", non-iterative, 10s/data"A", precision, 10s/data

(c)

(d)

Figure 1. Temperature sweep of “A” adhesive performed using non-iterative and precision sampling mode, respectively. Data collected at 5 s/data point (a), 10 s/data point (b), 20 s/data point (c), and 30

s/data point (d).

-100.0 -50.0 0 50.0 100.0 150.0 200.0 250.0temperature (°C)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G' (

Pa)

0

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

tan(delta)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G'' (

Pa)

"A", non-iterative, 20s/data"A", precision, 20s/data

-100.0 -50.0 0 50.0 100.0 150.0 200.0 250.0temperature (°C)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G' (

Pa)

0

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

tan(delta)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G'' (

Pa)

"A", non-iterative, 30s/data"A", precision, 30s/data

Table 1. Comparison of Precision and Non-iterative Sampling on Instrument Precision.

Non-iterative Sampling Precision Sampling

ΔTcalculated (°C)

Measured ΔT around Tg

(°C)

ΔTcalculated (°C)

Measured ΔT around Tg

(°C) 5 s/data point 0.42 0.8 0.42 2.7 10 s/data point 0.83 0.8 0.83 2.7 20 s/data point 1.67 1.6 1.67 2.7 30 s/data point 2.50 2.5 2.50 2.7

Table 1 shows that non-iterative sampling mode allows faster data acquisition than precision sampling. Using a 5ºC/min ramp rate, the measured temperature interval can keep up with the calculated temperature interval when the data acquisition rate is set for 10 s/data point in non-iterative sampling mode and 30 s/data point in precision sampling mode. Using the oscillation frequency of 6.28 rad/s in this experiment, a data acquisition rate of 5 s/data point was too fast for either non-iterative or precision sampling mode to maintain. The best temperature precision of the instrument at the experimental conditions of 5ºC/min ramp rate and 6.28 rad/s appears to be 0.8ºC. This precision can only be achieved by using non-iterative sampling mode at 10 s/data point acquisition rate. These experimental conditions were used for all subsequent temperature sweep experiments. The experiment also shows that non-iterative sampling mode is more suitable for measuring rapid transitions than precision sampling mode. Repeatability The repeatability of temperature sweep experiments was evaluated by running the experiment five times. Five specimens from the same adhesive sample were tested and the same set of experimental conditions was applied. Figure 2 is the overlay of five temperature sweeps of “A” adhesive run under the same conditions. This figure is also representative of “B” and “C” adhesives. One can see that the five scans overlay reasonably well throughout the temperature range. Table 2 lists the Tg and G'(25ºC) of “A”, “B”, and “C” adhesive, as measured from the temperature sweep experiments. Variation of the measured Tg for each adhesive was about 0.8ºC, which is the limitation of the instrument as shown in previous experiments. The standard deviations of Tg, obtained from five runs, were 0.44, 0.38, and 0.37ºC for the “A”, “B”, and “C” adhesives, respectively. These standard deviations are all less than the precision limit of the instrument, indicating that the experiments have very good reliability in measuring Tg. The variation of G'(25ºC) is in the 3000 Pa range, except that of adhesive “B”, for which the standard deviation of G'(25ºC) is only about 500 Pa. The magnitude of these standard deviations is very small, 2-5% of the measured values. Overall, the experiment has good repeatability and the instrument is reliable in measuring Tg and G'. Effect of Experimental Conditions The temperature sweep is run at a fixed temperature ramp rate and under a fixed oscillation frequency. In the industry, there is no standardized set of conditions for temperature sweep experiments. Various labs or individuals may use different ramp rates and oscillation frequencies for their testing. For the adhesive user, when adhesives are screened using manufacturer-supplied rheology data, it has been found that such data was obtained using different experimental conditions. It is of interest, then, to understand whether rheology results obtained using different sets of experimental conditions are

Figure 2. Repeatability of Temperature Sweep of “A” adhesive

Table 2. Repeatability of Temperature Sweep of “A”, “B”, and “C” Adhesive

Adhesive "A" Adhesive "B" Adhesive "C"

Sample # Tg (ºC)

G'(25ºC) (Pa)

Tg (ºC)

G'(25ºC) (Pa)

Tg (ºC)

G'(25ºC) (Pa)

1 -12.5 75225 -33.3 24540 -6.7 115700 2 -12.5 73026 -32.5 24920 -6.8 109200 3 -13.3 77335 -33.3 24910 -6.8 113000 4 -13.3 75050 -33.4 25100 -6.8 114800 5 -12.5 81923 -33.4 23790 -7.6 110500

Mean -12.8 76511 -33.2 24652 -6.9 112640 STD 0.44 3388 0.38 523 0.37 2765

comparable. Commonly used experimental conditions were examined, in this case ramp rates of 3ºC/min and 5ºC/min and frequencies of 6.28 rad/sec (1 Hz) and 10 rad/sec. The same set of data outputs, Tg and G'(25ºC), were used to quantitatively compare different combinations of experimental conditions. Table 3 summarizes Tg and G'(25ºC), as measured using different temperature ramp rates. It appears that temperature ramp rate had little impact on either Tg or G'(25°C). The differences in measured Tg, 0.3-0.5ºC, between these ramp rates are negligible when compared to the instrument precision of 0.8ºC. For all three adhesives, G'(25ºC) decreased slightly at the higher ramp rate. For the “B” and “C”

-100.0 -50.0 0 50.0 100.0 150.0 200.0 250.0temperature (°C)

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10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G' (

Pa)

0

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

tan(delta)

100.0

1000

10000

1.000E5

1.000E6

1.000E7

1.000E8

1.000E9

G'' (

Pa)

Run #1Run #2Run #3Run #4Run #5

adhesives this decrease was significant, exceeding the standard deviation found in prior repeatability experiments. The reason for this decrease is not yet understood.

Table 3. Tg and G'(25ºC) As Measured By Temperature Sweeps Using Different Temperature Ramp Rate at a Given Frequency

Adhesive Frequency (rad/s)

Ramp rate (ºC/min)

Tg (ºC)

G'(25ºC) (Pa)

Δ[G'(25ºC)] (Pa)

STD[G'(25ºC)](Pa)

6.28 3 -13.0 76560 1335 3388 A 6.28 5 -12.5 75225 6.28 3 -33.0 26690 2150 523 B 6.28 5 -33.3 24540 6.28 3 -7.0 92550 6765 2765 C 6.28 5 -6.7 85785

Table 4 shows the variation of measured Tg and G'(25ºC) with changes in frequency. As expected, there is a significant increase in both measured Tg and G'(25°C) at the higher frequency. This phenomenon is predicted by the principle of time-temperature superposition in viscoelastic materials, where a sample tested at higher frequency behaves as would a sample tested at a lower temperature. Table 4. Tg and G'(25ºC) As Measured By Temperature Sweeps Using Different Frequencies at a Given

Temperature Ramp Rate

Adhesive Frequency (rad/s)

Ramp rate (ºC/min)

Tg (ºC)

G'(25ºC) (Pa)

6.28 5 -12.5 75225 A 10 5 -11.1 89994

6.28 5 -33.3 24540 B 10 5 -31.7 30515

6.28 5 -6.7 85785 C 10 5 -6.3 93744

Frequency Sweep Repeatability (Single Specimen) Frequency sweeps are run by holding temperature constant and sampling data at stepped oscillation frequencies. In the industry, to extend the frequency range beyond that of the instrument, frequency sweeps are sometimes run at different temperatures and then overlaid using the principle of time-temperature superposition. The end result is a “master curve”, which can be used to compare adhesive performance over a wide frequency range. When running the frequency sweeps at different temperatures, the user has the option of using the same specimen for each sweep or changing the sample specimen between sweeps. To understand the consistency of frequency sweep measurements, both techniques were studied.

Three consecutive frequency sweeps were conducted at a single temperature over the same frequency range of 0.01 – 200 rad/s using a single specimen of adhesive “A”. Three different temperatures were used: 0, 25, and 50°C, and sample specimen was changed for each different temperature. Figure 3 shows the overlay of these experiments. For the most part, the scans overlay comparably to the prior temperature sweep repeatability experiments for adhesive “A”, but there is some obvious scatter in the 50°C curves at higher frequencies. Table 5 reports G' as measured at regular frequency intervals to provide a quantitative data comparison. Standard deviations of the G' values ranges from 4 – 10% of the mean value, except for the 50°C/100 rad/s case where the data becomes very unreliable. A phenomenon was also noted where each subsequent measurement of the same specimen shifts the G' curve slightly higher. The reason for this behavior is not well understood. It might be due to the internal stress generated from the previous sweep, and the conditioning time (4 minutes) might not be long enough for the adhesive to fully relax. More experiments need to be done to prove the above explanation.

0.01000 0.1000 1.000 10.00 100.0 1000ang. frequency (rad/s)

1000

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1.000E5

1.000E6

1.000E7

G' (

Pa)

0C, Freq sweep 1, Specimen 10C, Freq sweep 2, Specimen 10C, Freq sweep 3, Specimen 125C, Freq sweep 1, Specimen 125C, Freq sweep 2, Specimen 125C, Freq sweep 3, Specimen 150C, Freq sweep 1, Specimen 150C, Freq sweep 2, Specimen 150C, Freq sweep 3, Specimen 1

Figure 3. Repeatability of Frequency Sweeps Using a Single Specimen, “A” Adhesive

Repeatability (Multiple Specimens) The frequency sweeps were repeated on new specimens from the same adhesive sample at all three temperatures. Figure 4 compares the results for the new specimens to the frequency sweeps from the single specimen experiments. Table 6 compares the results from the new specimens to the mean values from the initial sets of frequency sweeps. The 0°C and 50°C data fall outside the standard deviation of the single specimen experiment over the entire frequency range. Only the 25°C data falls within the standard deviation of the single specimen, and even in this case the 100 rad/s data point is unreliable.

Table 5. Repeatability of Frequency Sweeps Using a Single Specimen, “A” Adhesive

Temperature (°C)

Frequency (rad/s)

G'(Run #1)(Pa)

G'(Run #2)(Pa)

G'(Run #3)(Pa)

Mean (Pa)

STD (Pa)

STD (% of Mean)

0 0.01 25490 28600 31060 28383 2791 9.8 0 0.1 57610 59910 65490 61003 4052 6.6 0 1 138300 141700 155300 145100 8996 6.2 0 10 394000 403900 440000 412633 24212 5.9 0 100 1350000 1462000 1594000 1468667 122137 8.3 25 0.01 8169 9186 9570 8975 724 8.1 25 0.1 18030 19300 20090 19140 1039 5.4 25 1 39800 41840 43590 41743 1897 4.5 25 10 86880 91410 95250 91180 4190 4.6 25 100 216900 230700 240000 229200 11623 5.1 50 0.01 4591 4881 5061 4844 237 4.9 50 0.1 7616 8023 8290 7976 339 4.3 50 1 15170 16330 16690 16063 794 4.9 50 10 32820 36810 37760 35797 2621 7.3 50 100 93470 50230 49450 64383 25193 39.1

0.01000 0.1000 1.000 10.00 100.0 1000ang. frequency (rad/s)

1000

10000

1.000E5

1.000E6

1.000E7

G' (

Pa)

0C Freq sweep 1, Specimen 10C Freq sweep 2, Specimen 10C Freq sweep 3, Specimen 10C Freq sweep 1, Specimen 225C Freq sweep 1, Specimen 125C Freq sweep 2, Specimen 125C Freq sweep 3, Specimen 125C Freq sweep 1, Specimen 250C Freq sweep 1, Specimen 150C Freq sweep 2, Specimen 150C Freq sweep 3, Specimen 150C Freq sweep 1, Specimen 2

Figure 4. Repeatability of Frequency Sweeps Using Multiple Specimens, “A” Adhesive

Table 6. Repeatability of Frequency Sweeps Using Multiple Specimens, “A” Adhesive

Temperature (°C)

Frequency (rad/s)

Mean G' (Specimen 1)

(Pa)

G' (Specimen 2)

(Pa)

ΔG' (Pa)

STD (Specimen 1)

(Pa) 0 0.01 28383 21160 7223 2791 0 0.1 61003 46440 14563 4052 0 1 145100 113000 32100 8996 0 10 412633 330500 82133 24212 0 100 1468667 1150000 318667 122137 25 0.01 8975 9402 -427 724 25 0.1 19140 19650 -510 1039 25 1 41743 41190 553 1897 25 10 91180 89220 1960 4190 25 100 229200 250100 -20900 11623 50 0.01 4844 5758 -914 237 50 0.1 7976 9520 -1544 339 50 1 16063 18830 -2767 794 50 10 35797 41460 -5663 2621 50 100 64383 92180 -27797 25193

Master Curves Frequency sweeps were run consecutively at 0, 25, and 50°C using a single sample of “A” adhesive. This data was used to generate a master curve by fixing the 25°C curve as a reference and shifting the 0°C and 50°C curves horizontally along the reduced frequency x-axis until the data effectively overlaps with the neighboring curves. The same technique was used to create a master curve from the multiple specimen repeatability data. The resultant master curves, including plots of both G' and tan δ, are presented in Figure 5. The single specimen data generates smoother curves, while the multiple specimen data does not overlay as well. It is apparent that higher frequency data is unreliable as it cannot be overlaid with adjacent curves in either case. When shifting curves of multiple specimen data, the experimenter encounters a situation in which improving the overlay of the G' curve causes greater incontinuity in the tan δ curve.

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

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1.E+08

-4 -3 -2 -1 0 1 2 3 4

Reduced Frequency (log rad/sec)

Shea

r Mod

ulus

(Pa)

0.1

1

10

100

Tan

Del

ta

Single Specimen

Multiple Specimen

Figure 5. “A” Adhesive Master Curves by Single and Multiple Specimen Frequency Sweeps Conclusions A stress-controlled rheometer can be a reliable instrument for the evaluation of pure solvent-based acrylic pressure sensitive adhesive properties. If Tg measurement is of interest from a strain controlled temperature sweep experiment, non-iterative sampling mode will generate the most precise data. In this type of experiment, G'(25°C) can be measured to within 5% accuracy and Tg measured accurately to the precision level of the instrument. Variation in temperature ramp rate has minimal effect on Tg and G'(25°C) measurement, while oscillation frequency has a statistically significant effect on both properties. Data generated by frequency sweeps of pressure sensitive adhesives is best acquired using a single sample specimen, and even then has a greater degree of variation than temperature sweep data, up to 10%. In some cases, high frequency (~100 rad/s) data is unreliable, and should be examined carefully before it is used to characterize PSA.