TCT Technical Papers
Recent Transpiration Studies
By Dr. Brian Alexander, Dr. Lesley Owens, Thomas Kozikowski (B.Sc.), and Dr. Paul Gaines, Inorganic Ventures.
At the conclusion of the initial transpiration studies, Inorganic Ventures researchers knew that transpiration rate was affected by bottle size and how frequently a bottle was opened, but additional questions remained:
 Is transpiration a function of temperature?
 Is the transpiration rate a function of the fill level of the bottle?
 What effects do container materials have on transpiration rates?
 Does cap torque affect transpiration rate?
 Do all products transpire at the same rate?
 Is transpiration rate a function of bottle geometry?
 Does water vapor only transpire around the cap or can it pass through bottle walls?
I. The Effect of Temperature
Warmer temperatures increase the evaporation rate for water, and the same effect is observed for transpiration. As storage temperatures increase, mass loss due to transpiration also increases (Fig. 1). Cold storage (~5 °C) of 125 mL lowdensity polyethylene (LDPE) bottles limits transpiration to less than 0.1% relative for at least 2 years.
Figure 1: The effect of temperature on transpiration for 125 mL LDPE bottles.
II. The Effect of Fill Level (How full is the bottle?)
Previous transpiration research indicated that halffull bottles transpired at a faster rate than full bottles (http://www.inorganicventures.com/tctoverview). For comparison purposes, it is useful to express the transpiration rate (%TR) as the percentage of mass lost per year:
%TR = (m / m_{CRM} t_{yr}) x 100  where:

Equation (1) 
Lowdensity polyethylene (LDPE) bottles of different sizes and different fill levels were stored at room temperature (20 °C) to determine the effect that bottle fill level has on transpiration rates. As expected, the less liquid a bottle contained the greater the transpiration rate (Fig. 2). The increase in transpiration rate as more of a CRM is used is significant enough that a 40% full 500 mL bottle and a 60% full 250 mL bottle will both transpire faster than a 100% full 125 mL bottle.
III. The Effect of Container Material
Inorganic Ventures recommends packaging many CRMs in lowdensity polyethylene bottles due to the cleanliness of LDPE (inorganicventures.com/containermaterialproperties). Occasionally, however, other container materials are preferred or necessary, frequently due to chemistry/compatibility issues (e.g., Hg stability in nitric acid, see inorganicventures.com/mercurychemicalstability).
Therefore, we compared transpiration rates for LDPE bottles to those measured for both highdensity polyethylene (HDPE) and glass bottles (Fig. 3). Of the three materials LDPE bottles had the highest transpiration rates. Glass bottles transpired the least, and HDPE bottles had transpiration rates that were slightly greater than glass. This relationship (LDPE_{%TR} > HDPE_{%TR} > Glass_{%TR}) was true for all bottle sizes, and the effects of bottle fill level observed for LDPE were also observed for HDPE and glass bottles.
IV. Does Cap Torque Affect Transpiration Rate?
Earlier transpiration studies indicated that most transpiration was occurring around the bottle cap. Therefore, it was important to consider if the torque applied when capping the bottle could affect transpiration rate. For this study an accelerated time study approach was used with LDPE bottles, and the calculations were based upon the Arrhenius equation where a rate increase of a factor of 3 was assumed for every 10 °C rise in temperature. The results indicated that capping bottles too tightly was as great a concern as loosely capped bottles (Fig. 4). The lowest transpiration rates were observed when the torque applied to the cap was between 510 lb·in (0.61.1 N·m).
V. Do all products transpire at the same rate?
Our studies indicate that transpiration only results in water loss from containers; we have not observed any loss of certified analytes from a CRM due to transpiration. However, the matrix of CRMs can vary widely, raising the question of whether the solution matrix has an effect on the transpiration rate. We studied four stock products that represented a wide range of different matrices:
Table 1. Stock products with range of matrices. 

Product 
Analyte 
Matrix 
ICF1 
1000 µg/mL Fluoride 
water 
CGCR10 
10000 µg/mL Chromium 
10% (v/v) HNO_{3} (7% HNO_{3} by weight) 
CGTE10 
10000 µg/mL Tellurium 
30% (v/v) HCl (11% HCl by weight) 
CGW10 
10000 µg/mL Tungsten 
2% (v/v) HNO_{3} / 6% (v/v) HF (1.4% HNO_{3} / 2.9% HF by weight) 
We compared the different products as stored in 125 mL LDPE bottles without TCT at 20 °C. The results indicate that the different products exhibited different transpiration rates (Fig. 5).
The wateronly matrix (fluoride) suffered the greatest mass loss due to transpiration, while the 30% HCl matrix (tellurium) transpired the least, at roughly half the rate of the water matrix. However, regardless of the matrix, storing the CRMs using TCT effectively prevented any significant transpiration from occurring (Fig. 6).
VI. Is transpiration rate a function of bottle geometry?
To determine if any correlations exist between bottle geometry and transpiration rates, we created a model for bottle geometry that considered three distinctly different regions of the bottle. The first is the wall of the bottle, the second is the region between the bottle threads and cap threads, and the third is the top and bottom of the bottle where the thickness is significantly greater than the walls. The following equations are used to calculate these regions in cm or cm2:
Bottle opening area = Πr_{c}^{2}  where r_{c}= bottle opening radius  Equation (2) 
Bottle opening circumference = Πd_{c}  where d_{c} = bottle opening diameter  Equation (3) 
Bottle 'side' area = Πd_{b}h_{b}  where d_{b} is bottle diameter; h_{b} = bottle height  Equation (4) 
Bottle crosssection area = Π(d_{b} / 2)^{2}  Equation (5)  
Bottle top area = Π(d_{b} / 2)^{2}  Πr_{c}^{2} (bottle crosssection area – bottle opening area)  Equation (6) 
Additional considerations regarding the mechanism of the transpiration were:
 Bottles remain upright and the cap opening has only vapor space above liquid. This is assumed to be a requirement for equations that may be able to predict past and future transpiration effects.
 The liquid/plastic interface may have a different transpiration rate than the vapor space/plastic interface, making the ‘fullness’ of the bottle a consideration.
 The bottle cap/vapor space interface may have a third transpiration rate.
We compared various bottle dimensions to measured transpiration rates to see if any correlations existed that could explain the transpiration effect. Transpiration rates (%TR) are expressed as mass loss in percent per year (Equation 1), and the bottle dimensions and transpiration rates included in the model are:
Table 2. Bottle dimensions and transpiration rates. 


LDPE 

HDPE 

Borosilicate Glass 

Bottle Parameters (cm, cm^{2}) 
125 mL 
250 mL 
500 mL 

125 mL 
250 mL 
500 mL 

125 mL 
250 mL 
500 mL 
Bottle opening diameter 
1.8 
1.8 
2.2 

1.8 
1.8 
2.2 

2.0 
2.0 
2.0 
Bottle opening circumference 
5.7 
5.7 
6.9 

5.7 
5.7 
6.9 

6.3 
6.3 
6.3 
Bottle opening area 
2.5 
2.5 
3.8 

2.5 
2.5 
3.8 

3.1 
3.1 
3.1 
(Bottle opening radius)^{2} 
0.81 
0.81 
1.2 

0.81 
0.81 
1.2 

1.0 
1.0 
1.0 
Bottle body diameter 
5.1 
6.2 
7.7 

5.1 
6.2 
7.7 

5.1 
6.17 
7.7 
Bottle body circumference 
16.0 
19.4 
24.2 

16.0 
19.4 
24.2 

16.0 
19.4 
24.2 
Bottle crosssection area 
20.4 
29.9 
46.5 

20.4 
29.9 
46.5 

20.4 
29.9 
46.5 
Bottle top area^{a} 
17.9 
27.4 
42.7 

17.9 
27.4 
42.7 

17.9 
27.4 
42.7 
Bottle body height 
7.3 
10.3 
13.3 

7.3 
10.3 
13.3 

7.3 
10.3 
13.3 
Bottle body surface area 
117 
200 
322 

117 
200 
322 

117 
200 
322 
(Bottle body radius)^{2} 
6.5 
9.5 
14.8 

6.5 
9.5 
14.8 

6.5 
9.5 
14.8 
Bottle liquid area^{b} 
109 
177 
311 

109 
177 
311 

109 
177 
311 
Transpiration Rate (%TR) 
0.254 
0.188 
0.132 

0.093 
0.061 
0.040 

0.077 
0.051 
0.017 
^{a}Bottle top area = Bottle crosssection area – Bottle opening area 

^{b}area of bottle covered by liquid assuming nominal fill level (e.g., 125 cm^{3}, 250 cm^{3}, etc.) 
To determine if a correlation existed, we compared the ratios of various bottle dimensions to the corresponding ratios of transpiration rates. In other words, if the transpiration rate for a 500 mL bottle was onehalf that observed for a 125 mL bottle, then we examined if certain bottle parameter ratios for a 500 mL bottle were also onehalf those for a 125 mL bottle. In previous research we observed a strong correlation between transpiration rates for LDPE bottles and the ratio of the circumference of the bottle opening to the surface area of the liquid. That same correlation was observed for this study, but we also observed correlations between transpiration rates and other bottle dimensions. The bottle parameters that most closely correlate with transpiration rates are listed below for LDPE (Table 3), HDPE (Table 4), and borosilicate glass (Table 5).
Table 3. LDPE bottle dimension ratios correlated with transpiration rates. 



Bottle Size 

Correlated Ratios 

Bottle Parameter Ratios 
125 mL 
250 mL 
500 mL 

125/500 mL 
250/500 mL 
500/500 mL 

Bottle opening circumference 
0.049 
0.029 
0.021 

2.3 
1.4 
1 

Bottle opening circumference 
0.052 
0.032 
0.022 

2.4 
1.5 
1 

Bottle opening circumference 
0.28 
0.19 
0.15 

1.9 
1.3 
1 

Bottle opening circumference 
0.32 
0.21 
0.16 

2.0 
1.3 
1 

Bottle opening area 
0.020 
0.010 
0.0076 

2.6 
1.3 
1 

Transpiration Rate (%TR) 
0.254 
0.188 
0.132 

1.92 
1.42 
1 

^{a} Volume liquid = nominal fill level (e.g., 125 cm^{3}, 250 cm^{3}, etc.) 

Table 4. HDPE bottle dimension ratios correlated with transpiration rates. 



Bottle Size 

Correlated Ratios 

Bottle Parameter Ratios 
125 mL 
250 mL 
500 mL 

125/500 mL 
250/500 mL 
500/500 mL 

Bottle opening circumference 
0.049 
0.029 
0.021 

2.3 
1.4 
1 

Bottle opening circumference 
0.052 
0.032 
0.022 

2.4 
1.5 
1 

Bottle opening circumference 
0.28 
0.19 
0.15 

1.9 
1.3 
1 

Bottle opening circumference 
0.32 
0.21 
0.16 

2.0 
1.3 
1 

Bottle opening area 
0.020 
0.010 
0.0076 

2.6 
1.3 
1 

Transpiration Rate (%TR) 
0.093 
0.061 
0.040 

2.3 
1.5 
1 

^{a} Volume liquid = nominal fill level (e.g., 125 cm^{3}, 250 cm^{3}, etc.) 

Table 5. Borosilicate bottle dimension ratios correlated with transpiration rates. 



Bottle Size 

Correlated Ratios 

Bottle Parameter Ratios 
125 mL 
250 mL 
500 mL 

125/500 mL 
250/500 mL 
500/500 mL 

Bottle opening circumference 
0.054 
0.032 
0.020 

2.7 
1.6 
1 

Bottle opening circumference 
0.058 
0.036 
0.020 

2.9 
1.8 
1 

Bottle opening circumference 
0.31 
0.21 
0.14 

2.2 
1.5 
1 

Bottle opening circumference 
0.35 
0.23 
0.15 

2.3 
1.5 
1 

Bottle opening area 
0.025 
0.012 
0.0062 

4.0 
1.9 
1 

Transpiration Rate (%TR) 
0.077 
0.051 
0.017 

4.5 
3.0 
1 

^{a} Volume liquid = nominal fill level (e.g., 125 cm^{3}, 250 cm^{3}, etc.) 

The three different bottle types all display different correlations between bottle dimensions/geometry and transpiration rate, and the most strongly correlated parameters are in bold text in Tables 35. It is interesting to note that while LDPE and HDPE bottles transpire at different rates, there is no difference between the two regarding bottle dimensions. LDPE bottles show the strongest correlations with transpiration rates when comparing the circumference of the bottle opening to either the crosssectional area of the bottle or the area of the bottle top. HDPE bottles correlate best when comparing the circumference of the bottle opening to either the total surface area of the bottle body or the area covered by liquid in a full bottle. For borosilicate bottles the only bottle parameter that comes close to correlating with transpiration rates is the ratio of bottle opening area to the volume of liquid.
The data indicates that transpiration rates are functions of bottle dimensions and geometry, and the fact that different correlations exist suggests that different mechanisms of transpiration are occurring for different bottle types.
VII. Does water vapor only transpire around the bottle cap or can it pass through bottle walls?
We cannot definitively answer that question with the data from this study, but there are arguments to suggest that transpiration can occur through the walls of LDPE and HDPE bottles. To our knowledge, transpiration through borosilicate glass has not been observed or described.
One factor is that if water vapor transpired solely through the bottle cap/opening then it would be reasonable to expect LDPE and HDPE bottles to have similar transpiration rates, particularly considering that LDPE and HDPE bottle caps are interchangeable, being both of the same size and material (polypropylene, PP). Another compelling consideration is that the packaging industry has described transpiration rates (typically referred to as moisture/water vapor transmission rates) for different polymers including LDPE and HDPE, and ASTM International has described several test methods for measuring transpiration effects in polymers and plastic films. While more research is necessary to completely characterize transpiration through the wall of a LDPE or HDPE bottle containing a CRM, it appears likely that the overall transpiration rates we observe are a function of both ‘aroundthecap’ and ‘throughthewall’ mechanisms.
Conclusions – The transpiration of water from polyethylene and borosilicate glass bottles can be significant enough to generate measureable systematic errors in the certified values of a CRM over time periods as short as a few months. Variables affecting the rate of transpiration include commonly expected ones such as the storage temperature, but other factors such as the torque applied to the cap are also important. The results of these studies are consistent with previous research (see http://inorganicventures.com/tctoverview for more information), and factors influencing transpiration rates can be summarized as follows:
 Storage temperature – lower storage temperatures decrease transpiration rates.
 Container material – observed transpiration rates are highest for LDPE, significantly lower for HDPE, and lowest for borosilicate glass. The distinct advantage of LDPE is that it is much cleaner than other commonly used plastics (including fluorinated polymers such as FEP and PFA).
 Container size – Regardless of the container material, smaller bottles transpire faster than larger bottles of the same material.
 Opening frequency – The more often a bottle is opened, the greater the transpiration rate.
 Container fill level – Transpiration rates increase as the amount of liquid in a bottle decreases.
 Cap torque – The torque applied to the cap of a bottle can have a significant effect on transpiration rates, to the extent that severely torqued caps generate accelerated transpiration rates.
 Solution matrix – The matrix of the solution stored in a bottle affects transpiration rates. Higher acid contents appear to inhibit transpiration, with pure water matrices exhibiting the highest transpiration rates.
 Container dimensions and geometry – Transpiration rates for different bottle materials correlate with different bottle regions, suggesting that the exact transpiration mechanisms are unique for different bottle materials.
 Cap vs. Walls? – Previous research concluded that transpiration around the bottle cap was the dominant mechanism for LDPE bottles. However, when combined with information from other industries, the data from this study for suggests that transpiration may also occur through the bottle walls for polyethylene containers. This effect is an active area of research to be addressed in future transpiration studies.
Future Work – While this research addressed several questions regarding the factors that affect transpiration rates, the data also raised additional questions. Future work at Inorganic Ventures regarding transpiration effects and mechanisms will include:
 Cap torque – More data is required to fully characterize this effect, and the initial study needs to be extended to incorporate HDPE and borosilicate bottles.
 Cap design? – The interface between the cap and the bottle appears critical in determining overall transpiration rates. Could a different cap material or cap design (e.g., a cap liner) decrease the transpiration rate?
 Matrix effect – The significance of the solution matrix upon transpiration rates seems evident, but this research focused on extremes in matrix composition (i.e., high acid contents compared to water). Characterizing intermediate matrices to fully describe this effect is warranted, which also raises the question ‘does the certified analyte and/or its concentration have any effect upon the transpiration rate?’.
 Cap vs. Walls – Isolating different bottle regions and measuring transpiration rates specific to these regions is a research focus, as the relative importance of the different bottle parts to overall transpiration rates is poorly characterized at this time.
 Can transpiration be predicted? – Is it possible to develop a mathematical relationship that would incorporate the dominant factors affecting transpiration rates? If so, could this equation be used to calculate transpiration rates with specified uncertainties?