Time-Dependent Testing Evaluation and Modeling for Rubber Stopper Seal Performance

Phase I: Compression Stress Relaxation (CSR) Testing and Modeling Fit

The CSR testing set-up is based on ISO 3384-1 Rubber, vulcanized or thermoplastic—Determination of stress relaxation in compression—Part 1: Testing at constant temperature, Method A. Instead of using typical cylindrical test button or O-ring samples, a testing sample assembly (Figure 3) is composed of a 20 mm rubber serum stopper plugged into a stainless steel fixture designed to dimensionally mimic a 20 mm glass vial (flange/neck/shoulder), both with and without an aluminum seal covering the stopper. For the testing sample assemblies covered with aluminum seals, the seals are not crimped onto the stainless steel vial fixture. The entire sample assembly is compressed between two flat metal plates and maintained at a fixed, constant 25% compression of the stopper flange thickness. The compression force vs time is continuously monitored for the duration of the testing. Basically, the test set-up and procedure are based on ISO 3384-1, but a modified rubber stopper sample assembly is used instead. The following is a summary of the test set-up:

• A temperature-controlled chamber maintained at 23 ± 1 °C is used for all sample conditioning and CSR testing.

• Samples are 20 mm serum stoppers with a nominal flange thickness of 3.33 mm. All of the test samples are conditioned at 23 ± 1 °C for at least 48 h before starting CSR testing.

• A stainless steel fixture designed to dimensionally mimic 20 mm glass vial (flange/neck/shoulder) holds each 20 mm stopper as shown in Figure 3.

• Two different sets of testing sample assemblies are evaluated. One set is with aluminum seals covered on stoppers, and another set is without aluminum seals, as shown in Figure 3. Multiple samples are tested for each set. For the sample assemblies covered with aluminum seals, a 20 mm West aluminum I-seal is used but is not crimped onto the 20 mm stainless steel fixture.

• Each sample is subject to a fixed, constant 25% compression of the stopper flange thickness throughout the entire testing duration. The 25% compression is precisely controlled and maintained by testing machine.

• Sample assemblies without aluminum seals are tested for 1000 h, whereas the sample assemblies with aluminum seals are tested for 1500 h. Note: the difference in test duration is due to equipment availability and the maintenance schedule.

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Figure 3

The compression force vs time is continuously tracked and recorded by computer throughout the entire duration of the experiment without subjective human interference during the testing.

After the CSR curves (force vs time) were collected, the CSR modeling fit calculations (force vs time) were applied based on the generalized Maxwell-Wiechert model of eq 2. This model is idealized with the assumptions of first-order linearity and derives from the set of linear ordinary differential equations of eq 1. In general terms, the viscoelastic rubber stopper material is assumed to have both Hookean elastic solid behavior (in which stress is a first-order linear approximation to strain deformation) and Newtonian viscous liquid behavior (in which stress is a first-order linear approximation to strain deformation rate) at the same time. In reality, the assumption of linearity may not match well with the observed test data because actual stress relaxation of the rubber stoppers can be much more complicated. This complication is likely due to the rubber stoppers' nonlinear viscoelastic nature under large compression deformation coupled with restrained geometry conditions of the sealed vial assembly. The theory of nonlinear viscoelasticity has been widely discussed in rubber polymer science and engineering (20,21,22). If the viscoelastic response of the stress relaxation is different from the typical exponential decay of eq 2, its viscoelasticity is likely no longer linear. There is no universal constitutive equation that can predict the nonlinear viscoelastic response of all the rubber polymer materials. Hence, the modeling fit is to be modified case by case. Based on our progress during the course of this study, the nonlinear Kohlrausch-Williams-Watts (KWW) function (20, 23, 24) was chosen to modify the exponential function of the generalized Maxwell-Wiechert model of eq 2. Setting N = 1, the modified model becomes: The KWW function is a stretched exponential function. The exponent β describes the breadth of the distribution in the limits of 0 < β ≤ 1. The β-term has been empirically associated (20,24,25,26) with rubber polymer molecules and molecule-to-molecule interactions including molecular structures, molecular weight, molecular weight distribution, crosslinking structure, crosslinking density, and so on, all of which affect the energy dissipated during stress relaxation. The nonlinear KWW stretched exponential equation has proven to be more appropriate in modeling polymer stress relaxation than the simple exponential equation in many modeling applications (20,24,25,26). The number N represents the degree of simulation complexity for the rubber polymer structure. The more complicated the structure, the larger number N is likely to be, which leads to more sophisticated modeling fit calculations and more computing iteration times. Based on progress from our modeling fit iterations during the course of the study, it was found that setting N = 1 for our case gave good modeling fit results without sacrificing valuable computation time. Equation 3 is the base of modeling fit for the study.

The modeling fit with the test data was carried out using following Maxwell-Wiechert model modified by the nonlinear KWW stretched exponential equation as per eq 3: where x₁, x₂, x₃, and x₄ are the parameters adopted to represent e₀E₀, e₀E₁, 1/τ₁, and β, respectively. The numerical modeling fit calculation uses the reduced gradient nonlinear method (27,28,29) by systematic iterations for the minimization of: where F_t = observed force and F_m = modeling force. F(x) is nonlinear. The reduced gradient method is to solve the partial differential equation matrix: by the following numerical iterations: Once all the final values (x₁, x₂, x₃, and x₄) have reached and satisfy ‖(∇F(x))‖ < ϵ, the numerical modeling fit is complete. Modeling fit based on eq 5 through eq 8 can process massive amount of testing data simultaneously from multiple testing curves collected from the same testing set-up. The modeling fit algorithm can be employed by the user as an investigation tool to calculate the sealing force throughout the entire sealed product life cycle.

Phase II: Residual Seal Force (RSF) Testing and Modeling

RSF is the force that a rubber closure flange exerts against the vial land seal surface of an assembled and capped CCS. RSF starts and continues immediately after a vial has been capped. However, once a vial has been capped, the RSF also starts to continuously decay. RSF is time-dependent, and the actual magnitude of RSF value depends on the timing when it is tested. The RSF of the sealed vial assemblies can be measured by an extensometer such as Instron (7, 8). Basically, it can be summarized to have four steps (8) to capture a single RSF data point as shown in Figure 4: (1) to test and collect the original compression data curve (force vs time) using an extensometer such as Instron, (2) to run the quadratic regression to minimize the testing noise and get the smoothed data curve from the original testing data curve, (3) to calculate the 2^nd derivative data curve from the smoothed data curve, and (4) to locate the unique RSF inflection data point on the original testing data curve by corresponding it to the absolute minimum of the 2^nd derivative at the exact same point on the time axis.

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Figure 4

The local quadratic regression smoothing is a linear regression (8, 27, 30) for Based on mathematical algorithm from typical textbooks (27, 30), using least squares for calculating the best a, b, and c values by minimizing the function, Solving equations ∂F/∂a = 0, ∂F/∂b = 0, and ∂F/∂c = 0. This is done with matrices. where

• F = compression force

• t = time

• a, b, and c are calculated smoothing parameters

Unlike CSR testing, which can be tested continuously on the same sample, RSF testing is a discrete test method for an individual sample because the internal stress-strain status within the sample assembly will change and redistribute immediately after the RSF measurement. Fundamentally, rubber polymer is a well-known viscoelastic material (12⇓⇓–15, 20⇓⇓⇓⇓⇓–26). Rubber has both elastic characteristic and viscous characteristic. As described in generalized Maxwell-Wiechert model (Figure 1), under constant compression percentage, the elastic stress portion is represented by springs, and the viscous stress portion is represented by dashpots and to be dissipated over time. The exponential decay of rubber CSR (either for CSR or RSF decay) is due to the viscous stress decay (related to dashpots in Figure 1). For RSF testing on a vial assembly, it has to enforce additional over-compression in order to generate a testing curve passing its RSF inflection point for subsequently calculating the RSF inflection point result (Figure 4). Theoretically, multiple RSF testing on a same vial sample by repetitively adding and removing additional compression percent to the original existing compression percentage within the same vial assembly, the elastic stress portion is fully recoverable regardless how many times of additional compression percentage and subsequent removal are repetitively going to be over the time. The viscous stress portion under additional compression percentage will be initially “returned” to certain level once the additional compression percentage is removed and the compression percentage recovered to the level at its original existing compression percent, but the viscous stress is not fully recoverable and there will be extra viscous stress dissipation in addition to its original decay from original existing compression percentage. The viscous stress will be completely dissipated and ultimately exhausted over the time, and the level-off portion of the relaxation curves in Figure 2 is mainly from elastic stress portion under a constant compression. In a schematic description, the more compression, the more and quicker piston displacement (Figure 1) within dashpot, leading to have more viscous stress dissipation. The more additional over compression, the more nonrecoverable viscous stress drop (dissipation) is going to be within the vial after each RSF testing on the same vial sample. Multiple RSF testing on the same vial assembly will artificially accelerate and create its own new viscous stress decay path much faster than its supposedly original viscous stress dissipation decay path and may rapidly advance and exhaust its viscous stress, and consequently make the decay curve level off faster. Multiple RSF testing on the same vial assembly will mess up the track of original RSF decay curve along its natural time axis, and it will be very difficult to establish the time-dependent modeling prediction without knowing its supposedly original RSF decay curve along its natural time axis.

However, multiple RSF testing on the same vial sample is supposedly not to destroy its ultimate RSF force (schematically level-off portion of Figure 2), but it just artificially messes up much-needed time track for time-dependent modeling fit and prediction. Because our intention is to construct an RSF relaxation decay trend for time-dependent modeling fit along the time axis, we choose to test undisrupted vial assemblies at each scheduled time point for time-dependent modeling fit. In order to do so, we had to seal thousands of vials in one single batch on the same day by using the same rubber stoppers, glass vials, aluminum seals, and crimping through the same capping process set-up, but tested each vial sample only once at a different time point and recorded it accordingly for time track and subsequently used the testing data for time-dependent modeling fit laer.

After thousands of RSF vial samples being made in a single batch, RSF testing is carried out by following a planned time schedule to pull out a group of ten sample assemblies each time from the same aforementioned sample batch. The RSF test data are recorded along the time axis for time-dependent evaluation and modeling. Here is the RSF testing set-up and procedure in detail:

• The laboratory temperature is maintained at 22 ± 1 °C for both sample conditioning and testing.

• Samples are 20 mm serum stoppers with a nominal flange thickness of 3.33 mm. These are the same stoppers used for CSR testing.

• Stoppers are placed into 20 mm, 10 mL Schott Standard glass vials.

• Vial and stopper assemblies are covered with 20 mm West aluminum I-seals. The same seal was also used for CSR testing.

• All testing samples are capped using a Genesis RW-4 #R425 capping machine with the exact same capping process set-up.

• A single batch of all the sample assemblies is made on the same day. A group of 10 sample assemblies is pulled out from the batch each time for RSF testing per the following time schedule:

  • Pull 10 samples every day for the first 2 weeks, excluding weekends and holidays.

  • Pull 10 samples at the end of third week and fourth week.

  • Pull 10 samples at the end of second month and third month.

• All the testing assemblies are conditioned at 22 ± 1 °C temperature all the time before starting the RSF testing.

• The RSF of the vial assemblies is measured by Instron (model 3345 with 500 N loadcell) at 0.05 cm/min compression speed, using Ludwig's method (8) and the same testing fixture design (Cap Anvil D) proposed by Ludwig (8).

After all the RSF data (force vs time) was collected, the RSF modeling fit calculation was applied based on eq 4 followed by the same reduced gradient nonlinear approach as shown by eq 5 through eq 8.