Diffusion-controlled toluene reference material for VOC emissions testing: International interlaboratory study

Figures & data

Figure 1. Reference film tiered loading chamber.

Figure 2. Sample holder with reference film.

Table 1. Chamber set points for reference material test method

Parameter	Small chamber set point	Large chamber set point
Air temperature (°C)	23	23
Relative humidity (%)	50	50
Small chamber airflow rate (m^3/hr)	0.055	0.30
Film surface area exposed per test (m^2)	0.0072	0.0144
Small chamber area specific airflow rate (m/hr)	7.6	21
Chamber background concentration (μg/m^3)	<2	<2

Figure 3. Determination of D and K from microbalance tests. (a) Fitting a Fickian diffusion model to the sorption and desorption data to get D. (b) Determining K by linear regression.

Table 2. Reported SCG laboratory compliance of test method specifications

Lab	Test #	Ship/storage temperature < 0°C	Sample age (days)	Used ILS calibrant	Mixing fan	Airflow (m^3/hr)	Temperature (°C)	RH (%)
A	1	Yes	14	Yes	Yes	0.055	23.2	47.5
A	2	Yes	14	Yes	Yes	0.054	23.2	47.5
B	1	Yes	2	Yes	No	0.055	23.0	50.0
B	2	Yes	8	Yes	No	0.055	22.6	50.0
C	1	Yes	23	No	No	0.055	23.0	45.0
C	2	Yes	30	No	No	0.055	23.0	45.0
D	1	Yes	8	Yes	No	0.049	22.6	50.2
D	2	Yes	14	Yes	No	0.049	22.5	50.2
E	1	Yes	36	Yes	No	0.054	23.5	51.3
E	2	Yes	42	Yes	No	0.055	22.7	51.8
F	1	Yes	1	Yes	Yes	0.055	22.9	50.0
F	2	Yes	8	Yes	Yes	0.055	22.9	50.0
F	3	Yes	21	Yes	Yes	0.055	22.9	50.0
G	1	Yes	7	Yes	No	0.055	22.5	49.9
G	2	Yes	11	Yes	No	0.055	23.1	50.0
H	1	No	19	No	No	0.055	23.0	49.3
H	2	No	22	No	No	0.055	23.0	47.8
I	1	Yes	1	Yes	No	0.055	23.3	51.7
I	2	Yes	7	Yes	No	0.055	23.1	50.8
J	1	Yes	7	Yes	No	0.055	24.2	49.8
J	2	No	29	Yes	No	0.055	23.0	50.0

Table 3. Small chamber group toluene concentrations at specified sampling time

	Sample time 24 hr		Sample time 48 hr		Sample time 72 hr
Lab	^a (μg/m^3)	u ^b (μg/m^3)	(μg/m^3)	u (μg/m^3)	(μg/m^3)	u (μg/m^3)
A	146.6	10.6	96.3	6.5	69.0	5.4
B	175.7	15.8	129.0	14.1	84.5	8.0
C	132.7	7.7	79.3	6.0	52.8	5.4
D	212.6 ^c	18.5	122.8	10.2	95.3	8.3
E	144.2	9.9	95.1	7.2	60.1	5.0
F	137.3	8.9	90.9	5.9	65.8	4.2
G	132.9	9.8	87.3	6.4	56.9	4.2
H	105.9	7.0	65.7	4.4	44.3	3.0
I	147.1	11.0	99.5	7.4	71.2	5.4
J	132.5	6.8	88.5	5.9	57.1	3.2
Total mean:	146.7 μg/m^3		95.4 μg/m^3		65.7 μg/m^3
SR ^d:	28.9 μg/m^3		18.8 μg/m^3		15.2 μg/m^3
RSD ^e:	19.7%		19.7%		23.1%
Model ^f:	141.9 ± 2.3 μg/m^3		85.1 ± 1.1 μg/m^3		52.8 ± 0.8 μg/m^3

Notes: ^a is the mean toluene concentration for both reference evaluations at time t; the individual concentration values at time t, x_it, are predictions from a linear

regression model that considers the concentration values of samples collected within 5 hr of sample time (e.g., 24 ± 5hr).

^bu is expanded uncertainty with coverage factor = 2.

^cValue is a suspected outlier.

^dS_R is between laboratory standard deviation.

^eRSD is relative standard deviation.

^fMass transfer model predicted chamber concentration averaged across all small chambers ± standard deviation.

Figure 4. Average concentration over all samples for each laboratory for target times 24, 48, and 72 hr. The error bars displayed are one standard deviation of the sample adjusted concentrations.

Figure 5. Youden plots for each sampling time point. The plotting characters represent the laboratories. The vertical line is the median value for sample 1 and the horizontal line is the median value for sample 2. The circle is a 95% confidence circle with a radius equal to 2.448 times the estimated standard deviation for a single result.

Table 4. Reported LCG laboratory compliance of test method specifications

Lab	Test number	Ship/storage temperature < 0°C	Sample age (days)	Used ILS calibrant	Mixing fan	Airflow (m^3/hr)	Temperature (° C)	RH (%)
K	1	No	21	Yes	Yes	0.3	23.0	46.6
K	2	No	28	Yes	Yes	0.3	22.8	48.0
L	1	Yes	7	Yes	Yes	0.3	23.2	53.3
L	2	Yes	14	Yes	Yes	0.3	23.2	53.8
M	1	Yes	8	Yes	Yes	0.3	23.0	48.2
M	2	Yes	15	Yes	Yes	0.3	23.1	48.0
N	1	No	8	Yes	Yes	0.3	23.1	51
N	2	No	14	Yes	Yes	0.3	23.1	51

Table 5. Large chamber group toluene concentrations at specified sampling time

	Sample time 24 hr		Sample time 48 hr		Sample time 72 hr
Lab	^a(μg/m^3)	u ^b (μg/m^3)	(μg/m^3)	u (μg/m^3)	(μg/m^3)	u (μg/m^3)
K	47.2	3.5	33.0	2.3	21.9	1.6
L	61.6	6.2	42.6	4.4	32.0	3.3
M	10.9	0.78	9.1	0.66	6.0	0.49
N	36.2	3.3	22.2	2.5	15.9	2.7
Total mean:	39.0 μg/m^3		26.7 μg/m^3		19.0 μg/m^3
SR ^c:	21.4 μg/m^3		14.4 μg/m^3		10.9 μg/m^3
RSD ^d:	54.9%		53.8%		57.5%
Model ^e:	53.7 ± 2.4 μg/m^3		31.9 ± 0.98 μg/m^3		19.8 ± 0.58 μg/m^3

Notes: ^a is the mean toluene concentration for both reference evaluations at time t; the individual concentration values at time t, x_it, are predictions from a linear regression model that considers the concentration values of samples collected within 5 hr of sample time (e.g., 24 ± 5hr).

^bu is expanded uncertainty with coverage factor = 2.

^cS_R is between laboratory standard deviation.

^dRSD is relative standard deviation.

^eMass transfer model predicted chamber concentration averaged across all large chambers ± standard deviation.

Figure 6. Large chamber group toluene concentrations measured at 24 hr, 48 hr, and 72 hr. The error bars displayed are one standard deviation of the sample adjusted concentrations.

Figure 7. Block plot for production tier (plotting characters) at 24 hr, 48 hr, and 72 hr.

Table 6. Frequencies of the relative order of the production tiers across SCG laboratories for each sample time point

	24 hr			48 hr			72 hr			Total
Prod. tier (i vs. j)	Freqency	Total	p-value ^a	Frequency	Total	p-value	Frequency	Total	p-value	Frequency	Total	p-value
1 vs. 2	3	5	1.00	4	5	0.375	2	5	1.00	9	15	0.607
1 vs. 3	2	2	0.50	1	2	1.00	0	2	0.50	3	6	1.00
2 vs. 3	2	5	1.00	3	5	1.00	3	5	1.00	8	15	1.00

^ap-value with n_i = n_j = 0.5.

Figure 8. NIST measured data compared to model prediction. Gray shadow represents model uncertainty.

Figure 9. Use of mechanistic mass transfer model to diagnose measurement discrepancies for Laboratory J during reference material emissions testing. Gray shadow represents model uncertainty.

Figure 10. Comparison of reference source emission rate average values.