Vial with optimized neck for improved side compression performance

1. A glass container, comprising:

a glass tube with a first end, a second end, and a longitudinal axis L tube therebetween, the glass tube has an outer surface and, in a direction from the first end to the second end, a top region, a junction region, a neck region, a shoulder region, and a body region, wherein the top region is at the first end and has an outer diameter (d t ), the neck region has an outer diameter (d n ) with d n <d t , the body region extends to the second end and has an outer diameter (d b ) with d b >d t , and the glass tube in the body region has a thickness (l b ); and

a glass bottom closing the glass tube at the second end,

wherein, when an outer surface of the body region is placed on a plane horizontal substrate, within a cross-section of the glass container that is located in a plane centrically located in the glass container and comprising the longitudinal axis L tube , f(x) defines a distance between the plane horizontal substrate and the outer surface of the glass tube at a position x and l(x) defines a thickness of the glass tube at the position x, wherein the thickness of the glass tube l(x) is measured for the position x in a direction perpendicular to the longitudinal axis L tube ,

wherein k(x)=|f″(x)/[1+f′(x) 2 ] 3/2 | defines an absolute value of a curvature of f(x) at a given position x; and

wherein, in an interval between x=P 1 and x=P 2 for a concave curvature in the interval between x=P 1 and x=P 2 , a minimum value for [l(x)/l b ] 3 /k(x) is at least 0.35 mm, wherein P 2 defines the x-position at which f(x) is ½×d b −¼×d t −¼×d n and P 1 is P 2 −d t /2+d n /2.

2. The glass container of claim 1 , wherein the junction region has another outer surface where the junction region merges into the neck region that is substantially circular arc-shaped, the substantially circular arc-shaped area having an outer radius r s , wherein the glass tube has a minimum thickness l n in the neck region, and wherein 2×[l n /l b ]×r s ≥0.9 mm.

3. The glass container of claim 2 , wherein the glass container is a vial having an interior volume of 1 to 8 ml, and d n ≥9.7 mm, and r s ≥0.5 mm.

4. The glass container of claim 3 , wherein the vial has a size designation “2R” or “4R” according to DIN EN ISO 8362-1:2016-06.

5. The glass container of claim 2 , wherein the glass container is a vial with an interior volume of 8.5 to 22 ml, d n ≥15.5 mm, and r s ≥0.5 mm.

6. The glass container of claim 5 , wherein the vial has a size designation “6R”, “8R” or “10R” according to DIN EN ISO 8362-1:2016-06.

7. The glass container of claim 2 , wherein the glass container is a vial with an interior volume of 22.5 to 150 ml, d n ≥16.5 mm, and r s ≥0.5 mm.

8. The glass container of claim 7 , wherein the vial has a size designation “20R”, “25R”, “30R”, “50R” or “100R” according to DIN EN ISO 8362-1:2016-06.

9. The glass container of claim 2 , wherein l n /l b ≥1.4.

10. The glass container of claim 2 , wherein l n ×r s /l b ≥0.7 mm.

11. The glass container of claim 1 , further comprising a pharmaceutical composition in an interior volume of the glass tube and a closure closing the glass tube at the first end.

12. The glass container of claim 1 , wherein the shoulder region has a shoulder angle α and wherein the shoulder angle α is in the range from 10° to 70° .

13. A plurality of glass containers, comprising:

each glass container having a glass tube with a first end and a second end and having a glass bottom closing the glass tube at the second end,

wherein the glass tube has an outer surface, a longitudinal axis L tube and has, in a direction from the first end to the second end, a top region, a junction region, a neck region, a shoulder region, and a body region,

wherein the top region is at the first end and has an outer diameter (d t ), the neck region has an outer diameter (d n ) with d n <d t , the body region extends to the second end and has an outer diameter (d b ) with d b >d t , and the glass tube in the body region has a thickness (l b ), and

wherein at least 75% of the glass containers in the plurality of glass containers fulfil a condition comprising:

when an outer surface of the body region is placed on a plane horizontal substrate, within a cross-section of the glass container that is located in a plane centrically located in the glass container and comprising the longitudinal axis L tube , f(x) defines a distance between the plane horizontal substrate and the outer surface of the glass tube at a position x and l(x) defines a thickness of the glass tube at the position x, wherein the thickness of the glass tube l(x) is measured for the position x in a direction perpendicular to the longitudinal axis L tube ,

wherein k(x)=|f″(x)/[1+f′(x) 2 ] 3/2 | defines an absolute value of a curvature of f(x) at a given position x; and

wherein, in an interval between x=P 1 and x=P 2 for a concave curvature in the interval between x=P 1 and x=P 2 , a minimum value for [l(x)/l b ] 3 /k(x) is at least 0.35 mm, wherein P 2 defines the x-position at which f(x) is ½×d b −¼×d t −¼×d n and P 1 is P 2 −d t /2+d n /2.

14. The plurality of glass containers of claim 13 , wherein at least 75% of the glass containers in the plurality of glass containers fulfil a condition comprising: the junction region has another outer surface where the junction region merges into the neck region that is substantially circular arc-shaped, the substantially circular arc-shaped area having an outer radius r s , wherein the glass tube has a minimum thickness l n in the neck region, and wherein 2×[l n /l b ]×r s ≥0.9 mm.

15. The plurality of glass containers of claim 13 , wherein each of the glass containers in the plurality of glass containers further comprise a pharmaceutical composition in an interior volume of the glass tube and a closure closing the glass tube at the first end.