Patent Publication Number: US-2023157927-A1

Title: Cap design for pharmaceutical container closure systems

Description:
This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Ser. No. 63/281,826, filed on Nov. 22, 2021, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present specification generally relates to container closure systems, such as glass or plastic containers for storing pharmaceutical products or biological materials. 
     BACKGROUND 
     Pharmaceutical containers, such as vials and syringes, are typically sealed via a stopper or other closure to preserve the integrity of the contained material. Closures, such as stoppers are typically made of synthetic rubbers and other elastomers. The stoppers are generally held in place with a cap crimped to the pharmaceutical container. Some biological materials (e.g., blood, serum, proteins, stem cells, and other perishable biological fluids) require storage at low temperatures, such as temperatures less than −45° C., less than −80° C., or even less than −180° C. For example, certain RNA-based vaccines may require storage at dry-ice temperatures (e.g., approximately −80° C.) or liquid nitrogen temperatures (e.g., approximately −180° C.) to remain active. Such low temperatures may result in dimensional changes in the closure components (e.g., the glass or plastic container, the stopper, an aluminium cap), leading to issues in the integrity of the seal, and potential contamination of the material stored therein. 
     SUMMARY 
     A first aspect of the present disclosure includes a cap for a sealing a pharmaceutical glass container. The cap comprises a cap skirt comprising an annular body and a crimp region at a first end of the annular body. The cap further comprises a top cover coupled to a second end of the cap skirt, the top cover comprising a solid disc or annular disc. The crimp region may comprise a crimpable metal. The annular body of the cap skirt comprises a coefficient of thermal expansion (CTE) greater than a CTE of a metal consisting of aluminum, a stiffness greater than or equal to 2 times a stiffness of the crimp region, or both. The CTE refers to the CTE at 20° C., and stiffness is defined as a Young&#39;s modulus times a cross-sectional area divided by an axial length. 
     A second aspect of the present disclosure may include the first aspect, wherein the CTE of the annular body of the cap skirt may be greater than the CTE of the metal consisting of aluminum by a difference of at least 100×10 −7  K −1 . 
     A third aspect of the present disclosure may include either one of the first or second aspects, wherein the CTE of the annular body of the cap skirt may be greater than or equal to 260×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , greater than or equal to 500×10 −7  K −1 , or even greater than or equal to 1,00×10 −7  K −1 . 
     A fourth aspect of the present disclosure may include any one of the first through third aspects, wherein the CTE of the annular body of the cap skirt may be greater than or equal to 260×10 −7  K −1  at a temperature less than or equal to the glass transition temperature of a stopper, such as less than or equal to −45° C. 
     A fifth aspect of the present disclosure may include any one of the first through fourth aspects, wherein the stiffness of the annular body of the cap skirt may be greater than or equal to 2 times a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. 
     A sixth aspect of the present disclosure may include any one of the first through fifth aspects, further comprising a stopper, wherein the stiffness of the annular body of the cap skirt may be within 30% of a stiffness of the stopper in a compressed state at temperatures less than or equal to the glass transition temperature T g  of the stopper. 
     A seventh aspect of the present disclosure may include any one of the first through sixth aspects, wherein the annular body of the cap skirt may have a Young&#39;s modulus of greater than or equal to 140 GPa, a radial thickness greater than or equal to 0.24 mm, or both. 
     An eighth aspect of the present disclosure may include any one of the first through seventh aspects, wherein the CTE of the annular body of the cap skirt may be greater than 260×10 −7  K −1  and the stiffness of the annular body is greater than 2 times a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. 
     A ninth aspect of the present disclosure may include any one of the first through eighth aspects, wherein the crimpable metal of the crimp region may comprise aluminum or an aluminum alloy. 
     A tenth aspect of the present disclosure may include any one of the first through ninth aspects, wherein the annular body of the cap skirt may comprise a metal or metal alloy having a CTE greater than the CTE of a metal consisting of aluminum. 
     An eleventh aspect of the present disclosure may include the tenth aspect, wherein the cap skirt may comprise a metal or metal alloy comprising one or more of zinc, aluminum, magnesium, copper, lithium, or combinations of these. 
     A twelfth aspect of the present disclosure may include any one of the first through eleventh aspects, wherein the cap skirt may comprise a polymer-metal composite structure. 
     A thirteenth aspect of the present disclosure may include the twelfth aspect, wherein the annular body of the cap skirt may comprise a polymer material and the crimp region may comprise the crimpable metal coupled to the polymer material of the annular body. 
     A fourteenth aspect of the present disclosure may include the thirteenth aspect, wherein the polymer material of the annular body may have a CTE of from 260×10 −7  K −1  to 3,000×10 −7  K −1 , such as from 280×10 −7  K −1  to 3,000×10 −7  K −1 , or even from 300×10 −7  K −1  to 3,000×10 −7  K −1 . 
     A fifteenth aspect of the present disclosure may include either one of the thirteenth or fourteenth aspects, wherein the annular body of the cap skirt may have a stiffness that is greater than or equal to 80% of a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. 
     A sixteenth aspect of the present disclosure may include any one of the thirteenth through fifteenth aspects, wherein the plastic material may comprise high density polyethylene, acrylonictile butadiene styrene copolymer, polypropylene, ultra-high molecular weight polyethylene, or combinations thereof. 
     A seventeenth aspect of the present disclosure may include any one of the first through sixteenth aspects, wherein the cap skirt may comprise an attachment flange disposed at a second end of the annular body and the top cover may be coupled to the attachment flange of the cap skirt. 
     An eighteenth aspect of the present disclosure may include the seventeenth aspect, wherein the top cover may be removable from the cap skirt. 
     A nineteenth aspect of the present disclosure may include any one of the first through eighteenth aspects, wherein the top cover may be formed integral with the annular body of the cap skirt to form a unitary cap. 
     A twentieth aspect of the present disclosure may include any one of the first through nineteenth aspects, wherein the top cover may comprise the annular disc having an axial opening in a center of the top cover. 
     A twenty-first aspect of the present disclosure may include any one of the first through twentieth aspects and may be directed to a sealed pharmaceutical container. The sealed pharmaceutical container comprises a glass container comprising a shoulder, a neck extending from the shoulder, and a flange extending from the neck. The flange comprises an underside surface extending from the neck, an outer surface extending from the underside surface, the outer surface defining an outer diameter of the flange, and a sealing surface extending between the outer surface and an inner surface defining an opening in the sealed pharmaceutical container. The sealed pharmaceutical container further comprises a sealing assembly comprising a stopper extending over the sealing surface of the flange of the glass container and covering the opening, and the cap of any one of the first through twentieth aspects. The cap secures the stopper to the flange. The sealing assembly maintains a helium leakage rate of the sealed pharmaceutical container of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to −45° C. 
     A twenty-second aspect of the present disclosure may include the twenty-first aspect, wherein the stopper may have a glass transition temperature (T g ) that is greater than or equal to −70° C. and less than or equal to −45° C. 
     A twenty-third aspect of the present disclosure may include the twenty-first aspect, wherein a glass transition temperature of the stopper may be less than or equal to −75° C. 
     A twenty-fourth aspect of the present disclosure may include any one of the twenty-first through twenty-third aspects, wherein the sealing assembly may maintain the helium leakage rate of the sealed pharmaceutical container of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to -80° C., less than or equal to −100° C., less than or equal to −120° C., or even less than or equal to −180° C. 
     A twenty-fifth aspect of the present disclosure may include any one of the twenty-first through twenty-fourth aspects, wherein the glass container may be constructed of a glass composition having a coefficient of thermal expansion that is greater than or equal to 0 and less than or equal to 70×10 −7  K −1 . 
     A twenty-sixth aspect of the present disclosure may include any one of the twenty-first through twenty-fifth aspects, wherein an absolute value of the difference between the CTE of the cap skirt and a CTE of the stopper may be less than or equal to 50×10 −7  K −1 . 
     A twenty-seventh aspect of the present disclosure may include any one of the twenty-first through twenty sixth aspects, wherein the CTE of the annular body of the cap skirt may be greater than a CTE of the stopper. 
     A twenty-eighth aspect of the present disclosure may include any one of the twenty-first through twenty-ninth aspects, wherein the annular body of the cap skirt may have a stiffness that is within 30% of a stiffness of the compressed rubber stopper at temperatures less than or equal to the glass transition temperature T g  of the stopper. 
     A twenty-ninth aspect of the present disclosure may include any one of the twenty-first through twenty-eighth aspects, wherein the sealed pharmaceutical container may maintain the helium leakage rate at is less than or equal to 1.4×10 −6  cm 3 /s as it is cooled to the temperature at a rate of less than or equal to 5° C. per minute. 
     A thirtieth aspect of the present disclosure may include the twenty-ninth aspect, wherein the cap may maintain continuous compression of the stopper against the flange of the glass container as the sealed pharmaceutical container is cooled. 
     A thirty-first aspect of the present disclosure may include any one of the twenty-first through thirtieth aspects, wherein the glass container may comprise an ion-exchangeable aluminosilicate glass, a Type 1B borosilicate glass, or a ion-exchangeable borosilicate glass. 
     A thirty-second aspect of the present disclosure may include any one of the first through thirty-first aspects and is directed to a method of sealing a sealed pharmaceutical container. The method comprises providing a pharmaceutical container comprising a shoulder, a neck extending from the shoulder and a flange extending from the neck. The flange may comprise an underside surface extending from the neck, an outer surface extending from the underside surface and defining an outer diameter of the flange, and an upper sealing surface extending from the outer surface to an inner surface of the sealed pharmaceutical container, wherein the inner surface defines an opening. The method may further include providing a sealing assembly comprising a stopper and the cap of any one of the first through twentieth aspects. The method may further include inserting a pharmaceutical composition into the pharmaceutical container, inserting the stopper into the opening so that the stopper extends over the upper sealing surface of the flange and covers the opening, and crimping the cap over the stopper and against the flange to thereby compress the stopper against the upper sealing surface. The method may further include cooling the sealed pharmaceutical container to a temperature of less than or equal to −45° C., wherein, after the cooling of the sealed pharmaceutical container, the compression is maintained on the sealing surface such that a helium leakage rate of the sealed pharmaceutical container is less than or equal to 1.4×10 −6  cm 3 /s at the temperature. 
     Additional features and advantages of the apparatus and methods described herein will be set forth in the detailed description which follows and, in part, will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments described herein, including the detailed description which follows, the claims, as well as the appended drawings. 
     It is to be understood that both the foregoing general description and the following detailed description describe various embodiments and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments, and are incorporated into and constitute a part of this specification. The drawings illustrate the various embodiments described herein, and together with the description serve to explain the principles and operations of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments set forth in the drawings are illustrative and exemplary in nature and not intended to limit the subject matter defined by the claims. The following detailed description of the illustrative embodiments can be understood when read in conjunction with the following drawings, where like structure is indicated with like reference numerals and in which: 
         FIG.  1    schematically depicts a cross-sectional view of a sealed pharmaceutical container, according to one or more embodiments described herein; 
         FIG.  2    schematically depicts a cross-sectional view of an upper portion of a glass container of the sealed pharmaceutical container of  FIG.  1   , according to one or more embodiments described herein; 
         FIG.  3    schematically depicts a cross-sectional view of an upper portion of another glass container, according to one or more embodiments described herein; 
         FIG.  4    schematically depicts a cross-sectional view of an upper portion of still another glass container, according to one or more embodiments described herein; 
         FIG.  5    schematically depicts a cross-sectional view of a sealing assembly of the sealed pharmaceutical container of  FIG.  1   , according to one or more embodiments described herein; 
         FIG.  6 A  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of 25° C., where the cap has a CTE of 256×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  6 B  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of 25° C., where the cap has a CTE of 352×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  6 C  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of 25° C., where the cap has a CTE of 698×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  7 A  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −80° C., where the cap has a CTE of 256×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  7 B  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −80° C., where the cap has a CTE of 352×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  7 C  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −80° C., where the cap has a CTE of 698×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  8 A  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  7 A , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  8 B  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  7 B , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  8 C  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  7 C , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  9 A  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −180° C., where the cap has a CTE of 256×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  9 B  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −180° C., where the cap has a CTE of 352×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  9 C  depicts a simulation of compression of a stopper against a flange of a glass container by a cap at a storage temperature of −180° C., where the cap has a CTE of 698×10 −7 /° C., according to one or more embodiments described herein; 
         FIG.  10 A  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  9 A , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  10 B  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  9 B , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  10 C  graphically depicts an interface between the stopper and the flange of the glass container in the simulation of  FIG.  9 C , where the differences in seal pressure are annotated using differences in shading patterns, according to one or more embodiments described herein; 
         FIG.  11    graphically depicts a plot of contact area (y-axis) between the flange and the stopper as a function of temperature (x-axis) for a plurality of sealed glass containers cooled at a constant cooling rate, where the sealing assemblies of the glass containers have caps with different CTEs when cooled at a first cooling rate, according to one or more embodiments described herein; 
         FIG.  12    graphically depicts a plot of contact area (y-axis) between the flange and the stopper as a function of temperature (x-axis) for a plurality of sealed glass containers cooled at a constant cooling rate, where the sealing assemblies of the sealed glass containers have caps with different stiffness, according to one or more embodiments described herein; 
         FIG.  13    graphically depicts a plot of contact area (y-axis) between the flange and the stopper as a function of temperature (x-axis) for a plurality of sealed glass containers cooled at a constant cooling rate, where the sealing assemblies of the sealed glass containers have caps with different CTE and stiffness, according to one or more embodiments described herein; 
         FIG.  14    schematically depicts a cross-sectional view of another embodiment of a cap of a sealing assembly for sealing a glass container, according to one or more embodiments described herein; 
         FIG.  15    schematically depicts a cross-sectional view of still another embodiment of a cap for a sealing assembly for sealing a glass container, according to one or more embodiments described herein 
         FIG.  16    schematically depicts a cross-sectional view of yet another embodiment of a cap for a sealing assembly for sealing a glass container, according to one or more embodiments described herein; 
         FIG.  17 A  depicts a simulation of compression of a stopper against a flange of a glass container by the cap of  FIG.  16    at a storage temperature of 25° C., where the cap skirt has a high CTE of 1264×10 −7  K −1  and increased stiffness, according to one or more embodiments described herein; 
         FIG.  17 B  depicts a simulation of compression of a stopper against a flange of a glass container by the cap of  FIG.  16    at a storage temperature of −80° C., where the cap skirt has a high CTE of 1264×10 −7  K −1  and increased stiffness, according to one or more embodiments described herein; 
         FIG.  17 C  depicts a simulation of compression of a stopper against a flange of a glass container by the cap of  FIG.  16    at a storage temperature of −180° C., where the cap skirt has a high CTE of 1264×10 −7  K −1  and increased stiffness, according to one or more embodiments described herein; 
         FIG.  18    graphically depicts a plot of contact area (y-axis) between the flange and the stopper as a function of temperature (x-axis) for a sealed glass container comprising the cap of  FIG.  16    having a CTE of 1264×10 −7  K −1  and thickness of 2.14 mm cooled at a constant cooling rate compared to a convention cap constructed of aluminum and having a thickness of 0.2 mm cooled at a constant cooling rate, according to one or more embodiments described herein. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to embodiments of sealed glass containers comprising sealing assemblies that maintain container closure integrity at low storage temperatures (e.g., less than or equal to −40° C., less than or equal to −50° C., less than or equal to −60° C., less than or equal to −70° C., less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., less than or equal to −180° C.). Referring now to  FIGS.  1  and  5   , embodiments of a sealed glass container  100  are schematically depicted. The sealed glass container  100  includes a glass container  102  and a sealing assembly  104  comprising a stopper  106  and a cap  108 . The present application is directed to designs for the cap  108  of the sealing assembly  104  that increase shrinkage of the cap  108  relative to the stopper  106  and flange  126  of the glass container  102 , increase the stiffness of the cap  108 , or both in order to maintain container closure integrity (CCI) at cryogenic storage temperatures, such as temperatures less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C. In embodiments, the cap  108  comprises a cap skirt  160  having a coefficient of thermal expansion (CTE) greater than a CTE of a metal consisting of aluminum, a stiffness greater than or equal to 2 times a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length, or both. The increased CTE, increased stiffness, or both of the cap skirt  160  of the cap  108  may increase the contact area, sealing pressure, or both between the stopper  106  and an upper sealing surface  110  of the glass container  102  at temperatures less than or equal to −40° C., less than or equal to −50° C., less than or equal to −60° C., less than or equal to −70° C., less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., less than or equal to −180° C. 
     As used herein, the term “surface roughness” refers to an Ra value or an Sa value. An Ra value is a measure of the arithmetic average value of a filtered roughness profile determined from deviations from a centerline of the filtered roughness. For example, an Ra value may be determined based on the relation: 
     
       
         
           
             
               
                 
                   
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     where H i  is a surface height measurement of the surface and Hu corresponds to a centerline (e.g., the center between maximum and minimum surface height values) surface height measurement among the data points of the filtered profile. An Sa value may be determined through an areal extrapolation of Equation 1 herein. Filter values (e.g., cutoff wavelengths) for determining the Ra or Sa values described herein may be found in ISO 25718 (2012). Surface height may be measured with a variety of tools, such as an optical interferometer, stylus-based profilometer, or laser confocal microscope. To assess the roughness of surfaces described herein (e.g., sealing surfaces or portions thereof), measurement regions should be used that are as large as is practical, to assess variability that may occur over large spatial scales. 
     As used herein, the term “container closure integrity” refers to maintenance of a seal at an interface between a glass container and a sealing assembly (e.g., between a sealing surface of a glass container and a stopper) that is free of gaps above a threshold size to maintain a probability of contaminant ingress or reduce the possibility of gas permeability below a predetermined threshold based on the material stored in a glass container. For example, in embodiments, a container closure integrity is maintained if a helium leakage rate during a helium leak test described in USP &lt;1207&gt; (2016) is maintained at less than or equal to 1.4×10 −6  cm 3 /s. 
     As used herein, the term “cryogenic storage temperature” refers to temperatures at which biomaterial, such as plant or animal cells, can be stored with indefinite longevity to the cells, while minimizing the level of freezing damage. As used herein, the term “cryogenic storage temperature” refers to temperatures greater than or equal to −80° C. 
     In embodiments of the glass containers described herein, the concentration of constituent components (e.g., SiO 2 , Al 2 O 3 , B 2 O 3  and the like) of the glass composition from which the glass containers are formed are specified in mole percent (mol. %) on an oxide basis, unless otherwise specified. 
     The term “substantially free,” when used to describe the concentration and/or absence of a particular constituent component in a glass composition, means that the constituent component is not intentionally added to the glass composition. However, the glass composition may contain traces of the constituent component as a contaminant or tramp constituent in amounts of less than 0.05 mol. %. 
     The term “CTE,” as used herein, refers to the coefficient of linear thermal expansion of a material at a temperature of 25° C., unless stated otherwise. 
     As used herein, the term “about” means that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art. When the term “about” is used in describing a value or an end-point of a range, the specific value or end-point referred to is included. Whether or not a numerical value or end-point of a range in the specification recites “about,” two embodiments are described: one modified by “about,” and one not modified by “about.” It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. 
     Directional terms as used herein - for example up, down, right, left, front, back, top, bottom—are made only with reference to the figures as drawn and are not intended to imply absolute orientation. 
     As used herein, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise. 
     Referring now to  FIG.  1   , one embodiment of a sealed glass container  100  for storing a pharmaceutical formulation is schematically depicted in cross-section. The sealed glass container  100  comprises a glass container  102  and a sealing assembly  104  coupled to the glass container  102  via an opening  105  of the glass container  102 . The sealing assembly  104  comprises a stopper  106  and a cap  108 . The stopper  106  may comprise an insertion portion  117  and a sealing portion  119 . The insertion portion  117  may be inserted into the opening  105  of the glass container  102  until the sealing portion  119  contacts an upper sealing surface  110  of the glass container  102 . The sealing portion  119  is then pressed against the upper sealing surface  110  via crimping of the cap  108  to the glass container  102  to form a seal at the upper sealing surface  110 . Various aspects of the glass container  102  and the sealing assembly  104  are designed to ensure maintenance of container closure integrity of the glass container  102  at low storage temperatures, as described herein. 
     The glass container  102  generally comprises a body  112 . The body  112  extends between an inner surface  114  and an outer surface  116  of the glass container  102  and includes a center axis C. The body  112  encloses an interior volume  118  of the glass container  102 . In the embodiment of the glass container  102  shown in  FIG.  1   , the body  112  comprises a wall portion  120  and a floor portion  122 . The wall portion  120  transitions into the floor portion  122  through a heel portion  124 . In embodiments, the glass container  102  includes a flange  126 , a neck  128  extending from the flange  126 , a barrel  115 , and a shoulder  130  extending between the neck  128  and the barrel  115 . The floor portion  122  is coupled to the barrel  115  via the heel portion  124 . In embodiments, the glass container  102  is symmetrical about the center axis C, with each of the barrel  115 , neck  128 , and flange  126 , being substantially cylindrical-shaped. 
     The body  112  has a wall thickness T w  which is defined as the distance between the inner surface  114  and the outer surface  116 , as depicted in  FIG.  1   . The wall thickness T w  of the glass container  102  may vary depending on the implementation. In embodiments, the wall thickness T w  of the glass container  102  may be less than or equal to 6 millimetres (mm), such as less than or equal to 4 mm, less than or equal to 2 mm, less than or equal to 1.5 mm or less than or equal to 1 mm. In embodiments, the wall thickness T w  may be greater than or equal to 0.1 mm and less than or equal to 6 mm, greater than or equal to 0.3 mm and less than or equal to 4 mm, greater than or equal to 0.5 mm and less than or equal to 4 mm, greater than or equal to 0.5 mm and less than or equal to 2 mm, or greater than or equal to 0.5 mm and less than or equal to 1.5 mm. In embodiments, the wall thickness T w  may be greater than or equal to 0.9 mm and less than or equal to 1.8 mm. The wall thickness T w  may vary depending on the axial location within the glass container  102 . 
     In embodiments, the glass container  102  may be formed from Type I, Type II or Type III glass as defined in USP &lt;660&gt;, including borosilicate glass compositions such as Type 1B borosilicate glass compositions under USP &lt;660&gt;. In embodiments, the glass container  102  may be formed from ion-exchangeable borosilicate glass composition, such as those described in co-pending U.S. application Ser. No. 16/533,954, filed Aug. 7, 2019 and entitled “Ion Exchangeable Borosilicate Glass Compositions and Glass Articles Formed from the Same” assigned to Corning Incorporated, hereby incorporated by references in its entirety. Alternatively, the glass container  102  may be formed from alkali aluminosilicate glass compositions such as those disclosed in U.S. Pat. No. 8,551,898, hereby incorporated by reference in its entirety, or alkaline earth aluminosilicate glasses such as those described in U.S. Pat. No. 9,145,329, hereby incorporated by reference in its entirety. In embodiments, the glass container  102  may be constructed from a soda lime glass composition. In embodiments, the glass container  102  is constructed of a glass composition having a coefficient of thermal expansion that is greater than or equal to 0 K −1  and less than or equal to 100×10 −7  K −1  (e.g., greater than or equal to 30×10 −7  K −1  and less than or equal to 70×10 −7  K −1 ). In embodiments, the glass container  102  may comprise a glass composition having a coefficient of thermal expansion that is greater than or equal to 0 K −1  and less than or equal to 70×10 −7  K −1 . 
     While the glass container  102  is depicted in  FIG.  1    as having a specific form-factor (i.e., a vial), it should be understood that the glass container  102  may have other form factors, including, without limitation, Vacutainers®, cartridges, syringes, ampoules, bottles, flasks, phials, tubes, beakers, or the like. Further, it should be understood that the glass containers  102  described herein may be used for a variety of applications including, without limitation, as pharmaceutical packages, beverage containers, or the like. 
     Referring again to  FIG.  1   , the flange  126  of the glass container  102  can comprise the upper sealing surface  110 , an underside surface  132 , and an outer surface  134 . The outer surface  134  may define an outer diameter of the flange  126 . The upper sealing surface  110  is the surface of the flange  126  that contacts the stopper  106  to form a fluid tight seal between the stopper  106  and the flange  126 . Referring to  FIGS.  2 - 4   , the upper sealing surface  110  of the flange  126  of the glass container  102  may have different configurations. Referring to  FIG.  2   , in embodiments, the upper sealing surface  110  may comprise an inclined sealing surface  140 . The inclined sealing surface  140  may extend at least part way or all the way between the outer surface  134  of the flange  126  and the inner surface  114  of the glass container  102 . The inclined sealing surface  140  may extend at an angle  150  relative to a plane  152  extending through an end  154  of the opening  105 . The plane  152  may be a planar surface that rests on top of the glass container  102  at the opening  105  (e.g., that rests on peaks of the inclined sealing surface  140 ). In embodiments, the plane  152  may connect points extending around the upper sealing surface  110  that are most distant from a reference point (e.g., the floor portion  122 , see  FIG.  1   ) of the glass container  102 . The plane  152  may extend through the top of the glass container  102  in a direction perpendicular to the center axis C of the glass container  102  (e.g., in the X-Y plane of the coordinate axis in  FIG.  2   ). In embodiments, the plane  152  extends perpendicular to the portion of the inner surface  114  defining the opening  105 . The angle  150 , as described herein, may be referred to as a “flange angle.” In embodiments, the angle  150  is greater than 5 degrees and less than or equal to 45 degrees. 
     Referring now to  FIG.  3   , in embodiments, the glass container  102  may include an upper sealing surface  110  that extends in the plane  152  extending through the end  154  of the opening  105  in the glass container  102 . In embodiments, the upper sealing surface  110  may extend substantially perpendicular (e.g., at an angle greater than or equal to 89.5 degrees and less than or equal to 90.5 degrees) to the center axis C of the glass container  102 . In embodiments, the upper sealing surface  110  may extend substantially perpendicular to the inner surface  114  of the glass container  102 , the inner surface  114  defining the opening  105 . Such an upper sealing surface  110  may increase a contact area between the stopper  106  (see  FIG.  1   ) and the upper sealing surface  110 , which may increase the probability of maintaining integrity of the seal. 
     In the glass container  102  depicted in  FIG.  3   , the upper sealing surface  110  extends from the outer surface  134  to the inner surface  114 . It should be appreciated that the upper sealing surface  110  may include a variety of different features consistent with the present disclosure. Referring now to  FIG.  4   , in embodiments, the upper sealing surface  110  of the glass container  102  may include flat portion  136 , a chamfer  137 , a rounded corner  138 , or combinations of these. When present, the chamfer  137  may extend between the flat portion  136  and the outer surface  134  of the flange  126 . When present, the rounded corner  138  may extend between the flat portion  136  and the inner surface  114 . In embodiments, the flat portion  136  may extend in the plane  152 , as described in relation to the upper sealing surface  110  in  FIG.  3   . In other embodiments, the flat portion  136  may be angled relative to plane  152 , as described in relation to the upper sealing surface  110  shown in  FIG.  2   . In embodiments, the chamfer  137  may extends at an angle of 45 degrees relative to the flat portion  136 . In embodiments, the chamfer  137  may increase the integrity of the seal created by the stopper  106  by allowing the stopper  106  to encapsulate the upper sealing surface  110  in multiple directions. In embodiments, instead of the rounded corner  138 , the upper sealing surface  110  may include an inner chamfer similar extending between the flat portion  136  and the inner surface  114 , the second chamfer having features similar to those described for chamfer  137 . It should be appreciated that any of the features (e.g., the chamfer  137 , the rounded corner  138 , or other sealing feature) described herein with respect to  FIG.  4    may also be incorporated into the inclined sealing surface  140  described herein with respect to  FIG.  2    (e.g., the upper sealing surface  110  that forms an angle  150  with the plane  152  may comprise a chamfer extending between the inclined sealing surface  140  and the outer surface  134 , a rounded corner  138  extending between the inclined sealing surface  140  and the inner surface  114 , or both the chamfer  137  and the rounded corner  138 ). 
     Referring now to  FIG.  5   , the sealed glass container  100  includes the sealing assembly  104  attachable to the glass container  102  at least in part through engagement with the opening  105  of the glass container  102 . The sealing assembly  104  includes the stopper  106  and the cap  108 . The stopper  106  may comprise an insertion portion  117  and a sealing portion  119 . The insertion portion  117  may be inserted into the opening  105  of the glass container  102  until the sealing portion  119  contacts the upper sealing surface  110  of the glass container  102 . The stopper  106  may be made from a resilient material that is able to be compressed by the cap  108  during sealing. In embodiments, the stopper  106  may be constructed of synthetic rubbers or other elastomers. Such materials beneficially have high permeation resistance and elasticity to facilitate insertion of the stopper  106  into the glass container  102  to seal the interior of the glass container  102 . Synthetic rubbers may include, but are not limited to butyl rubbers or other synthetic rubbers. 
     The cap  108  may be a metal-containing cap. Referring again to  FIG.  5   , the cap  108  may include a cap skirt  160  and a cap cover  170  coupled to the cap skirt  160 . The cap skirt  160  may include at least an annular body  162  and a crimp region  164  disposed at one axial end of the annular body  162 . The cap skirt  160  may further include an attachment flange  166  coupled to the other axial end of the annular body  162 . The annular body  162  of the cap skirt  160  may have an inner surface  168  and an outer surface  169 . The inner surface  168  may face radially inward towards the flange  126  of the glass container  102  and may contact portions of the outer surface  134  of the flange  126 , portions of the stopper  106 , or both when the sealing assembly  104  is installed on the glass container  102 . The outer surface  169  of the annular body  162  may face radially outward away from the flange  126  of the glass container  102 . A thickness t CS  of the annular body  162  of the cap skirt  160  is the distance between two opposing points on the inner surface  168  and the outer surface  169  of the annular body  162 . 
     Referring again to  FIG.  5   , the attachment flange  166  may be configured to engage with the cap cover  170  to couple the cap cover  170  to the cap skirt  160 . In embodiments, the attachment flange  166  may be an annular flange that extends from the annular body  162  radially inward towards axis A of the glass container  102 . The attachment flange  166  may be disposed at an end of the annular body  162  opposite the end comprising the crimp region  164 . 
     The crimp region  164  may be disposed at a bottom end of the annular body  162  of the cap skirt  160 . The bottom end of the annular body  162  refers to the end of the annular body  162  oriented in the −Z direction of the coordinate axis of  FIG.  5   . The crimp region  164  may be constructed of a crimpable metal, such as aluminum metal or an alloy of aluminum. Any other crimpable metal may be suitable for constructing the crimp region  164  of the cap skirt  160 . 
     The cap  108  may be placed over the stopper  106  and around the flange  126  of the glass container  102 . The cap  108  may be crimped to the flange  126 . Crimping the cap  108  to the flange  126  includes deforming the crimp region  164  of the cap skirt  160  around the underside surface  132  of the flange  126  so that the cap  108  compresses the stopper  106 , which presses the sealing portion  119  of the stopper  106  against the upper sealing surface  110  of the flange  126  to form a seal between the upper sealing surface  110  of the flange  126  and the sealing portion  119  of the stopper  106 . In embodiments, the cap  108  of the sealing assembly  104  is crimped around the flange  126  of the glass container  102  via any suitable crimping method (e.g., a pneumatic crimping apparatus or the like). During the sealing process, the stopper  106  is inserted into the opening  105  in the glass container  102 , and a compression force is applied to the cap  108  during crimping. For example, as depicted in  FIG.  5   , the cap  108  comprises the crimp region  164  that contacts the underside surface  132  of the flange  126  to force the stopper  106  to remain in a compressed state and form a seal after the crimping process. Compression of the stopper  106  generates a residual sealing force within the flange  126  that maintains compression on the stopper  106  after the cap  108  is crimped into place. In embodiments, the crimp region  164  of the cap  108  that directly contacts the underside surface  132  of the flange  126  possesses a length  111  that is greater than or equal to 1 mm to facilitate maintenance of residual sealing force within the stopper  106  at storage temperatures of less than or equal to −80° C. 
     Cooling of existing sealed containers to cryogenic storage temperatures less than or equal to −80° C., for example, may cause loss of seal integrity between the stopper and the glass container. Without being bound by any particular theory, it is believed that loss of seal integrity at temperatures less than or equal to −80° C. may be caused by differences in thermal shrinkage between various components, loss of resiliency of the stopper at temperatures less than the glass transition temperature of the material from which the stopper is made, or a combination of these. 
     When the sealed glass container  100  is cooled to relatively low storage temperatures of less than or equal to −80° C. (e.g., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C.), each of the constituent components of the sealed glass container  100  may undergo a volumetric shrinkage that is dependent on the thermal properties of that component. As depicted in  FIG.  5   , the volume of material disposed between the crimp region  164  of the cap skirt  160  and the attachment flange  166  or top cover  170  of the cap  108  comprises the sealing portion  119  of the stopper  106  and the flange  126  of the glass container  102 . If the combination of the stopper  106  and the flange  126  shrinks in an amount that is greater than the amount of shrinkage of the cap  108 , the compression on the stopper  106  provided by the cap  108  may diminish, which increases the probability of the seal at the upper sealing surface  110  being broken. 
     Referring again to  FIG.  5   , the combined height  154  (e.g., in the +/−Z direction of the coordinate axis of  FIG.  5   ) of the flange  126  (flange height  156 ) and compressed stopper  106  (stopper height  158  when the stopper  106  is compressed by the cap  108 ) is approximately equal to the axial length of the annular body  162  (e.g., the distance between the crimp region  164  and the attachment flange  166  of the cap skirt  160  of the cap  108 ). When crimped, the cap  108  may compress the stopper  106  against the upper sealing surface  110  to form a seal. If the combined height  154  shrinks to a greater extent than the annular body  162  of the cap skirt  160 , however, the compression of the stopper  106  may diminish, reducing the residual sealing force. To maintain a compression of the stopper  106 , the shrinkage ΔL of the annular body  162  of the cap  108 , the sealing portion  119  of the stopper  106 , and the flange  126  of the glass container  102  may satisfy the relation in Equation (1). 
       Δ L   cap   ≥ΔL   flange   +ΔL   stopper    (1)
 
     In Equation 1, the shrinkage ΔL of each component may be approximated by the relationship in Equation (2). 
       Δ L=L   i ×( e   ∫α(T) −1),   (2)
 
     In Equation (2), L i  is an initial dimension of the component and α(T) is the temperature-dependent CTE of the material out of which each of the cap  108 , the stopper  106 , and the glass container  102  are constructed. 
     Further compounding the problem, the stopper  106  may lose elasticity at temperatures less than or equal to −80° C. The stopper  106  may be constructed of a polymer-based material (e.g., butyl or other synthetic rubbers). Each of these materials may have glass a transition temperature (T g ). Below the T g , the material of the stopper  106  may behave as a solid (e.g., loss of elasticity), resulting in a diminished sealing force at the upper sealing surface  110  of the flange  126 . For example, if the stopper  106  is cooled to a temperature less than or equal to its T g , the stopper  106  may not fill the entirety of the gap between the upper sealing surface  110  and the attachment flange  166  or top cover  170  of the cap  108 , thereby increasing the probability of the seal breaking. That is, the stopper  106  effectively behaves as two different materials as it is cooled below its glass transition temperature: an elastic material above the transition temperature, and a solid glass below the transition temperature. Using Equation (2) above, the shrinkage of the stopper  106  disposed between the flange  126  and the attachment flange  166  or top cover  170  of the cap  108 , when cooled from an initial temperature T i  greater than T g  to a final temperature T F  less than T g , may be approximated according to Equation 3. 
     
       
         
           
             
               
                 
                   
                     Δ 
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                                     glass 
                                   
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     In Equation 3, α glass  refers to the CTE of the glass-like material that the rubber of the stopper  106  transforms into below its glass transition temperature T g . 
     In embodiments, to maintain the seal, the cap  108  and stopper  106  may be constructed such that the shrinkage of the cap  108  is greater than or equal to the combined shrinkage of the stopper  106  and the flange  126  of the glass container  102 . Typical commercially available sealing assemblies for glass containers generally include metal crimp cap that consists entirely of aluminum metal. The aluminum crimp cap encompasses the rubber stopper and the flange of the glass container. Typical aluminum crimp caps that consist entirely of aluminum metal do not have a coefficient of thermal expansion (CTE) that is great enough to maintain the sealing force of the stopper against the upper sealing surface of the flange of the glass container when cooled to temperatures less than or equal to −80° C. (e.g., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C.). Typical crimp caps consisting entirely of aluminium metal may have a CTE of approximately 255×10 −7  K −1  at 20° C. Typical rubbers out of which the stopper  106  is constructed (e.g., Butyl 325, Butyl 035, etc.) may have CTEs of greater than or equal to 300×10 −7  K −1 . That is, purely in terms of CTE differential, the crimp caps consisting entirely of aluminum metal have a tendency to shrink less than the stopper, resulting in a diminished sealing force at lower storage temperatures of less than or equal to −80° C. Further, the Young&#39;s modulus (the resistance to deformation) of existing aluminum crimp caps is not high enough to maintain the sealing force of the stopper against the upper sealing surface of the flange of the glass container. 
     The present application is directed to designs for the cap  108  of the sealing assembly 104 that increase shrinkage of the cap  108  relative to the stopper  106  and flange  126  of the glass container  102 , increase the stiffness of the cap  108 , or both in order to maintain container closure integrity (CCI) at temperatures less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C. In embodiments, the relationship between CTE and stiffness of the cap  108  may be defined to ensure container closure integrity (CCI) at temperatures from −80° C. to −180° C., and even less than or equal to −180° C. To facilitate meeting such a relationship, the shrinkage of the cap  108  may be increased, the stiffness of the cap  108  may be increased, or both. In embodiments, the cap  108 , in particular the cap skirt  160  of the cap  108 , may have a CTE that is at least 100×10 −7  K −1  greater than the CTE of existing caps or cap skirts consisting of aluminum metal, which has a CTE of approximately 255×10 −7  K −1  at 20° C. In embodiments, the cap  108 , in particular the cap skirt  160  of the cap  108 , may have a CTE that is at least 100×10 −7  K −1  greater than the CTE of existing caps or cap skirts consisting of aluminum metal at temperatures less than or equal to the glass transition temperature T g  of the stopper  106  (e.g., less than or equal to −45° C.). In embodiments, the cap  108  or cap skirt  160  of the cap  108  of the present disclosure may have a stiffness that is at least 2 times the stiffness of existing aluminum crimp caps consisting of aluminum metal and having a radial thickness of 0.19 mm and an identical axial length, such as a stiffness of greater than or equal to 140 GPa. In embodiments, the cap  108  or cap skirt  160  of the cap  108  may have a CTE greater than a CTE of a metal consisting of aluminum and a stiffness greater than the stiffness of existing aluminum crimp caps consisting of aluminum metal and having a radial thickness of 0.19 mm and an identical axial length. 
     The cap  108  structures disclosed herein can maintain continuous compression of the stopper  106  against the upper sealing surface  110  of the flange  126  of the glass container  102  as the sealed pharmaceutical container  100  is cooled. Maintaining continuous compression of the stopper  106  against the flange  126  during cooling may maintain container closure integrity (CCI) during cooling to temperatures less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C. As previously discussed, CCI can be evaluated by conducting a helium leak test as described in USP &lt;1207&gt; (2016). The sealed glass container  100  comprising the caps  108  disclosed herein can maintain the helium leakage rate at is less than or equal to 1.4×10 −6  cm 3 /s as it the sealed glass container  100  is cooled to the temperature at a rate of less than or equal to 5° C. per minute. 
     The sealing assembly  104  comprising the caps  108  disclosed herein can maintain a helium leakage rate of the sealed glass container  100  of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to −45° C. The sealing assembly  104  comprising the caps  108  disclosed herein can maintain a helium leakage rate of the sealed glass container  100  of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to −80° C. The sealing assembly  104  comprising the caps  108  disclosed herein can maintain a helium leakage rate of the sealed glass container  100  of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to −100° C., less than or equal to −120° C., less than or equal to −150° C., or even less than or equal to −180° C. 
     Referring again to  FIG.  5   , as previously discussed, the cap  108  comprises the cap skirt  160  and the top cover  170 . The cap skirt  160  includes the annular body  162 , the crimp region  164  at the bottom end of the annular body  162  (e.g., the end of the annular body  162  in the −Z direction of the coordinate axis in  FIG.  5   ), and the attachment flange  166  at the top end of the annular body  162  opposite from the crimp region  164 . The top cover  170  may be shaped like a solid disc or an annular disc and may be constructed of a polymeric material. In embodiments, the top cover  170  may be an annular disc having an axial opening (not shown) extending axially (e.g., in the +/−Z direction of the figures) through the top cover  170 . The axial opening may provide access to the stopper  106  through the cap  108  so that a syringe can be utilized to penetrate through the stopper  106  to remove the contents of the sealed glass container  100  without removing the cap  108  and stopper  106  from the glass container  102 . The top cover  170  may be coupled to the attachment flange  166  of the cap skirt  160 . 
     The crimp region  164  may comprise a crimpable metal. Crimpable metals are metals that are able to be crimped using commercially available crimping devices. In embodiments, the crimpable metal of the crimp region  164  may comprise aluminum or an aluminum alloy. 
     In embodiments, the cap skirt  160  may have a CTE greater than a CTE of a metal consisting of aluminium. In embodiments, the annular body  162  of the cap skirt  160  may have a CTE greater than a CTE of a metal consisting of aluminium. The greater CTE of the annular body  162  of the cap skirt  160  may increase the shrinkage of the cap skirt  160  when the sealed glass container  100  is cooled, which may enable the cap  108  to exert greater sealing force on the stopper  106  as the sealed glass container  100  is cooled to temperatures less than or equal to −80° C., less than or equal to −100° C., less than or equal to −125° C., less than or equal to −150° C., less than or equal to −175° C., or even less than or equal to −180° C. 
     Referring now to  FIGS.  6 A,  6 B, and  6 C , the seal pressure between the stopper  106  and the upper sealing surface  110  of the flange  126  of the glass container  102  at different CTE values of the cap skirt  160  and at different temperatures is simulated. The seal pressure at 25° C. is simulated for cap skirts  162  having a CTE of 256×10 −7  K −1  ( FIG.  6 A ), a CTE of 352×10 −7  K −1  ( FIG.  6 B ), and a CTE of 698×10 −7  K −1 . As shown in  FIGS.  6 A- 6 C , each of the simulations show substantial seal pressure along the entire interface between the stopper  106  and the upper sealing surface  110  at 25° C. At 25° C., there is very little difference in the seal pressure as a function of CTE of the cap skirt  162 . 
     Referring now to  FIGS.  7 A,  7 B, and  7 C , the simulations are repeated for each of the cap skirts  162  at a temperature of −80° C. Referring to  FIGS.  8 A,  8 B, and  8 C , close-ups of the interface between the stopper  106  and the flange  126  of the glass container  102  are graphically depicted and the different seal pressure regions illustrated with different shade patterns to better show the difference in seal pressures and contact areas. As shown in  FIG.  8 A , for the cap skirt  162  having a CTE of 256×10 −7  K −1 , the seal pressure is shown to be greatly reduced and the regions of no seal pressure (e.g., less than 0.0001) are increased compared to the simulation at 25° C. in  FIG.  6 A .  FIG.  8 A  shows a large portion of the interface between the stopper  106  and the upper sealing surface  110  having zero seal pressure. Referring to  FIG.  8 B , when the CTE of the cap skirt  162  is increased to 352×10 −7  K −1 , a greater portion of the interface between the stopper  106  and the upper sealing surface  110  has a positive seal pressure and the seal pressure in these regions is greater at −80° C. compared to the seal pressure profile achieved with the cap skirt  162  having CTE of 256×10 −7  K −1  of  FIG.  8 A . Referring now to  FIG.  8 C , when the CTE of the cap skirt  162  is increased to 698×10 −7  K −1 , the seal pressure extends across a much greater percentage of the width of the upper sealing surface  110  compared to the lower CTE simulations in  FIGS.  8 A and  8 B  at the temperature of −80° C. Further, with CTE of 698×10 −7  K −1 , the contract pressure is greater in magnitude compared to the lower CTE simulations of  FIGS.  8 A and  8 B  at the temperature of −80° C. 
     Referring now to  FIGS.  9 A,  9 B, and  9 C , the simulations are repeated for each of the cap skirts  162  at a temperature of −180° C. Referring to  FIGS.  10 A,  10 B, and  10 C , close-ups of the interface between the stopper  106  and the flange  126  of the glass container  102  are graphically depicted and the different seal pressure regions illustrated with different shade patterns to better show the difference in seal pressures and contact areas. As shown in  FIG.  10 A , for the cap skirt  162  having a CTE of 256×10 −7  K −1 , the regions of no seal pressure (e.g., less than 0.0001) are increased compared to the simulation at −80° C. in  FIG.  8 A .  FIG.  10 A  shows seal pressure only at the outer edge of the upper sealing surface  110 , which greatly increases the probability of losing container closure integrity during cooling. Referring to  FIG.  10 B , when the CTE of the cap skirt  162  is increased to 352×10 −7  K −1 , a greater portion of the interface between the stopper  106  and the upper sealing surface  110  has a positive seal pressure and the seal pressure in these regions is greater at −180° C. compared to the seal pressure profile achieved with the cap skirt  162  having CTE of 256×10 −7  K −1  of  FIG.  10 A . The two regions of seal pressure shown in  FIG.  10 B  can greatly reduce the probability of CCI failure at −180° C. compared to the single point of seal pressure shown in  FIG.  10 A . Referring now to  FIG.  10 C , when the CTE of the cap skirt  162  is increased to 698×10 −7  K −1 , the seal pressure extends across a much greater percentage of the width of the upper sealing surface  110  compared to the lower CTE simulations in  FIGS.  10 A and  10 B  at the temperature of −180° C. Further, with CTE of 698×10 −7  K −1 , the seal pressure is greater in magnitude compared to the lower CTE simulations of  FIGS.  10 A and  10 B  at the temperature of −180° C. 
     Referring now to  FIG.  11   , the contact area (y-axis) between the stopper  106  and the upper sealing surface  110  as a function of temperature (x-axis) is graphically depicted for cap skirts  162  having different CTE ranging from 236×10 −7  K −1  to 1160×10 −7  K −1 . As shown in  FIG.  11   , at a CTE of 236×10 −7  K −1 , the contact area between the stopper  106  and the upper sealing surface  100  is less than 25 mm 2  at temperatures less than −90° C. As the CTE of the cap skirt  162  is increased, the contact area between the stopper  106  and the upper sealing surface  100  increases. Increasing the CTE of the cap skirt  162  to just 352×10 −7  K −1  more than doubles the contact area between the stopper  106  and upper sealing surface  100  compared to the contact area with the CTE of 236×10 −7  K −1 . The contact area continues to increase as the CTE of the cap skirt  162  is increased. These simulations demonstrate that increasing the CTE of the cap skirt  162  can increase the seal pressure and contact area between the stopper  106  and the upper sealing surface  110  of the flange  126  at decreasing temperatures down to at least −180° C. This increase in seal pressure and contact area resulting in increasing the CTE of the cap skirt  162  can reduce the probability of CCI failure at temperatures less than −80° C. 
     Referring again to  FIG.  5   , in embodiments, the cap skirt  160 , in particular, the annular body  162  of the cap skirt  160 , may have a CTE that is greater than the CTE of existing metal crimp caps. The cap skirt  160 , in particular the annular body of the cap skirt  160 , may comprise a material having a CTE that is greater than the CTE of a typical crimp cap consisting of aluminum. In embodiments, the cap skirt  160 , in particular the annular body  162 , may comprise a material having a CTE that is greater than the CTE of a metal consisting of aluminum metal (e.g., at least 99% aluminum) by a difference of at least 100×10 −7  K −1 . In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may comprise a material having a CTE that is greater than a CTE of the stopper  106 . In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may comprise a material having a CTE such that an absolute value of the difference between the CTE of the cap skirt  160  or annular body  162  and the CTE of the stopper is less than or equal to 50×10 −7  K −1 . Typical stoppers  106  can have CTE at 20° C. of from 1311×10 −7  K −1  to 3134×10 −7  K −1 . In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may comprise a material having a CTE that satisfies the following Equation 4, in which α skirt  is the CTE of the cap skirt  160  at the glass transition temperature of the stopper  106 , α stopper  is the CTE of the stopper  106  at the glass transition temperature of the stopper  106 , α flange  is the CTE of the flange  126  of the glass container  102  at the glass transition temperature of the stopper  106 , h stopper  is the height of the stopper  106  encompassed by the cap skirt  160 , and h flange  is the height of the flange  126 . 
     
       
         
           
             
               
                 
                   
                     α 
                     skirt 
                   
                   ≥ 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             
                               α 
                               stopper 
                             
                             × 
                             
                               h 
                               stopper 
                             
                           
                           + 
                           
                             
                               α 
                               flange 
                             
                             × 
                             
                               h 
                               flange 
                             
                           
                         
                         ) 
                       
                       
                         ( 
                         
                           
                             h 
                             stopper 
                           
                           + 
                           
                             h 
                             flange 
                           
                         
                         ) 
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In embodiments, the cap skirt  162  or the annular body  162  of the cap skirt  160  may comprise a material having a CTE that is greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 . In embodiments, the cap skirt  162  or the annular body  162  of the cap skirt  160  may comprise a material having a CTE that is greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1  at temperatures less than or equal to the glass transition temperature of the stopper  106  (e.g., less than or equal to −45° C.). 
     In embodiments, the greater CTE of the annular body  162  of the cap skirt  160  may be achieved by constructing the cap skirt  160 , or portions thereof, from a material having a CTE greater than aluminum metal (e.g., greater than 255×10 −7  K −1  at 20° C.). The material of the cap skirt  160 , in particular the annular body  162 , may comprise a material selected from a metal, a metal alloy, or a polymer-metal composite, where the material has a high CTE of greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 . 
     In embodiments, the cap skirt  160  or the annular body  162  of the cap skirt  160  may comprise a metal or metal alloy having a CTE greater than the CTE of aluminum metal (i.e., a metal consisting of aluminium), such as a CTE greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 . In embodiments, the metal or metal alloy may have a CTE greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1  at temperatures less than or equal to the glass transition temperature T g  of the stopper  106  (e.g., less than or equal to about −45° C.). In embodiments, the cap skirt  160  can be made of a high CTE metal that can be crimped. Examples of high CTE metals that can be crimped include, but are not limited to, Li, Li-containing alloys, Pb, Sb—Pb alloys, Zn, Zn-containing alloys, Zn—Pb—Cd alloys, Cd, or combinations of these. However, some of these high CTE metals may be unstable in the atmosphere or may pose unacceptable health and safety risks. 
     Therefore, in embodiments, the cap skirt  160  can be constructed of a composite material comprising aluminum metal or high CTE metal alloy comprising one or more of zinc (Zn), aluminum (Al), magnesium (Mg), copper (Cu), or combinations of these. In embodiments, the cap skirt  160 , or the annular body  162  of the cap skirt  160 , may comprise Zn or Mg to increase the CTE of the cap relative to aluminum. In embodiments, the cap skirt  160  or the annular body  162  of the cap skirt  160  may comprise a metal alloy comprising one or more of zinc, aluminum, magnesium, copper, or combinations of these. In embodiments, the cap skirt  160 , or the annular body  162  of the cap skirt  160 , may comprise an alloy of Zn, such as a Zn alloy comprising one or more metals selected from the group consisting of Al, Mg, Cu, and combinations of these. Alloys of Zn may have CTE that can be as much as 15% greater than the CTE of a metal consisting of aluminum. In embodiments, the metal alloy of the cap skirt  160 , or the annular body  162  of the cap skirt  160 , may comprise less than or equal to 5 wt. % Al. In embodiments, the metal-containing cap  108  may comprise other metallic alloys, such as a suitable Pb-Sn alloy. In embodiments, the high CTE metal or metal alloy of the cap skirt  160  may be a crimpable metal or metal alloy. Metals and metallic alloys may beneficially be used with existing crimping processes. As such, current bottling processes need not be significantly modified to obtain the improved seals described herein. 
     In embodiments, the entire cap skirt  160 , including the annular body  162 , the crimp region  164 , and the attachment flange  166 , may be constructed of the high CTE metal alloy, such as any of the high CTE metal alloys previously described herein. In embodiments, the annular body  162  of the cap skirt  160  may comprise the high CTE metal alloy, and the crimp region  164 , the attachment flange  166 , or both may comprises a metal or metal alloy that is different from the high CTE metal alloy of the annular body  162 . 
     In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may be constructed of a polymer-metal composite material. In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may be constructed of a metal-polymer composite comprising a polymer matrix coated with a metal-containing coating. In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may be constructed of a metal-polymer composite comprising a metal matrix having polymer-based reinforcements disposed therein. The polymer-based reinforcements may be dispersed throughout the aluminum matrix. In these embodiments, the polymer may have a high CTE, such as a CTE of greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , greater than or equal to 500×10 −7  K −1  , or even greater than or equal to 1000×10 −7  K −1  (at 20° C. and/or at temperatures less than or equal to the glass transition temperature of the stopper  106 ) so that the CTE of the polymer-metal composite material is greater than the CTE of aluminum metal (i.e., metal consisting of aluminum). The metal of the polymer-metal composite materials may any of the metals or metal alloys previously discussed herein. In embodiments, the metal of the polymer-metal composite materials may be aluminum or an aluminum-containing alloy. 
     Referring again to  FIG.  5   , in embodiment, the cap  108  may be a polymer-metal composite structure comprising a polymer having a high CTE and a crimpable metal for the crimp region  164  of the cap skirt  160 . In particular, the cap  108  may include the cap skirt  160  that may be a polymer-metal composite structure. In embodiments, the annular body  162  of the cap skirt  160  may comprise a polymer having a high CTE, and the crimp region  164  of the cap skirt  160  may comprise a crimpable metal, such as an aluminum-containing metal, coupled to the polymer of the annular body  162 . Aluminum-containing metals may include aluminum metal or an aluminum-containing metal alloy. The crimpable metal of the crimp region  164  may be coupled directly to the polymer material of the annular body  162  at the bottom end of the annular body  162  (e.g., the end of the annular body  162  oriented in the −Z direction of the coordinate axis in  FIG.  5   ). In embodiments, the crimp region  164  comprising the crimpable metal may be molded into the polymer material of the annular body  162 . 
     The annular body  162  may comprise a polymer having a high CTE that is greater than the CTE of a metal consisting of aluminum. In embodiments, the attachment flange  166  may also comprise the polymer material having high CTE. The polymer material of the annular body  162  may have a CTE of greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , greater than or equal to 500×10 −7  K −1 , or even greater than or equal to 1,000×10 −7  K −1 . In embodiments, The polymer material of the annular body  162  may have a CTE of greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 355×10 −7  K −1 , greater than or equal to 400×10 −7  K −1 , greater than or equal to 500×10 −7  K −1 , or even greater than or equal to 1,00×10 −7  K −1  at temperatures less than or equal to the glass transition temperature T g  of the stopper  106  (e.g., ≤−45° C.). The polymer may have a CTE of less than or equal to 3,000×10 −7  K −1 , such as less than or equal to 2500×10 −7  K −1 , or less than or equal to 2000×10 −7  K −1 . In embodiments, the polymer of the annular body  162  may have a CTE of from greater than 255×10 −7  K −1  to 3000×10 −7  K −1 , from 260×10-7 K −1  to 3000×10 −7  K −1 , from 260×10 −7  K −1  to 2500×10 −7  K −1 , from 260×10 −7  K −1  to 2000×10 −7  K −1 , from 300×10-7 K −1  to 3000×10 −7  K −1 , from 300×10 −7  K −1  to 2500×10 −7  K −1 , from 300×10 −7  K −1  to 2000×10 −7  K −1 , from 350×10-7 K −1  to 3000×10 −7  K −1 , from 350×10 −7  K −1  to 2500×10 −7  /K, from 350×10 −7  K −1  to 2000×10 −7  K −1 , from 400×10-7 K −1  to 3000×10 −7  K −1 , from 400×10 −7  K −1  to 2500×10 −7  K −1 , from 400×10 −7  K −1  to 2000×10 −7  K −1 , from 500×10−7 K −1  to 3000×10 −7  K −1 , from 500×10 −7  K −1  to 2500×10 −7  K −1 , or from 500×10 −7  K −1  to 2000×10 −7  K −1 . 
     The polymer material for the annular body  162  of the cap skirt  160  may be any polymer having a high CTE greater in the above ranges, such as but not limited to high density polyethylene (HDPE), acrylonitrile butadiene styrene polymer (ABS), polypropylene (PP), ultra-high molecular weight polyethylene (UHMWPE), or other high CTE polymers. In embodiments, the polymer material may be a high CTE plastic. In embodiments, the annular body  162  of the cap skirt  160  may comprise a polymer selected from the group consisting of HDPE, ABS, PP, UHMWPE, and combinations thereof. 
     For most common polymer materials, the Young&#39;s modulus of the polymer material is very low compared to metals used for existing metal crimp caps, even though the polymer materials can have a much greater CTE compared to the metals. The reduced Young&#39;s modulus of the polymer material may result in a reduction in stiffness of the cap skirt  160 , which may cause the cap skirt  160  to flex during cooling. The flexing of the cap skirt  160  during cooling may reduce the amount of force exerted by the cap  108  on the stopper  106 , thereby increasing the probability of loss of CCI when the sealed glass container  100  is cooled to temperatures less than −80° C. Thus, any benefit to the sealing force provided by the increase in CTE of the polymer material may be reduced due to the reduced stiffness of the polymer material. 
     Referring now to  FIG.  14   , to ensure the polymer portions of the cap skirt  160  are strong enough to enable the cap  108  to hold the stopper  108  tightly against the upper sealing surface  110  with sufficient sealing force, the stiffness of the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may be increased. The stiffness of the annular body  162  of the cap skirt  160  can be increased by increasing the radial thickness t CS  of the annular body  162  of the cap skirt  160 . The radial thickness t CS  of the annular body  162  may be the distance between the inner surface  168  of the annular body  162  and the outer surface  169  of the annular body along a radial line perpendicular to the center axis C of the sealed glass container  100  and extending radially outward from center axis C. The stiffness of the annular body  162  is defined by the following Equation 5. 
     
       
         
           
             
               
                 
                   k 
                   = 
                   
                     E 
                     × 
                     
                       A 
                       L 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In Equation 5, k is the stiffness, E is the Young&#39;s modulus, A is the cross-sectional area of the annular body  162  of the cap skirt  160 , and L is the axial length of the annular body  162  of the cap skirt  160 . The cross-sectional area A is the cross-section taken by a plane that is perpendicular to the center axis C of the sealed glass container  102 . The length L of the annular body  162  is the length of the annular body  162  in a direction parallel to the center axis C of the sealed glass container  100  (i.e., in the +/−Z direction of the coordinate axis in  FIG.  14   ). 
     The annular body  162  of the cap skirt  160  may have a stiffness that is within 20% of a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length L. In other words, an absolute difference between the stiffness of the polymeric annular body  162  of the cap skirt  160  and the stiffness of the comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length L is less than or equal to 20% of the stiffness of the comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length L. A ratio of the stiffness of the annular body  162  of the cap skirt  160  to the stiffness of the comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length L may be greater than 0.8, such as from 0.8 to 1.2. 
     In embodiments, the annular body  162  of the cap skirt  160  may have a stiffness that is within 30% of a stiffness of the compressed rubber stopper  106  at temperatures less than or equal to the glass transition temperature T g  of the stopper  106  (e.g., ≤−45° C.). Considering the need to maintain 20% of the seal surface of the rubber stopper  106  on the upper sealing surface  110  of the flange  126 , the stiffness of the annular body  162  of the cap skirt  160  can be estimated from the following Equation 6. 
     
       
         
           
             
               
                 
                   0.7 
                   ≤ 
                   
                     
                       
                         ( 
                         
                           
                             E 
                             polymer 
                           
                           × 
                           
                             A 
                             polymer 
                           
                         
                         ) 
                       
                       × 
                       
                         L 
                         stopper 
                       
                     
                     
                       
                         ( 
                         
                           
                             E 
                             stopper 
                           
                           × 
                           
                             A 
                             
                               flange 
                               ⁢ 
                                   
                               top 
                               ⁢ 
                                   
                               surface 
                             
                           
                           × 
                           0.2 
                         
                         ) 
                       
                       × 
                       
                         L 
                         polymer 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In Equation 6, E polymer  and A polymer  are the Young&#39;s modulus and area, respectively, of the annular body  162  constructed of the polymer material, E stopper  is the Young&#39;s modulus of the stopper  106 , A flange top surface  is the seal surface area of the upper sealing surface  110  of the flange  126  of the glass container  102 , L stopper  is the axial length of the stopper  106 , and L polymer  is the axial length of the cap skirt. In most cases, an inner radius of the annular body  162  comprising the polymer material is about the same as the inner radius of the comparable cap skirt annular body consisting of aluminum metal. Thus, one method to change the stiffness is to change the thickness δt of the annular body  162  comprising the polymer material. Equation 6 can be approximated by the following Equation 7. 
     
       
         
           
             
               
                 
                   0.7 
                   ≤ 
                   
                     
                       
                         ( 
                         
                           
                             E 
                             polymer 
                           
                           × 
                           δ 
                           ⁢ 
                           
                             t 
                             polymer 
                           
                         
                         ) 
                       
                       × 
                       
                         L 
                         stopper 
                       
                     
                     
                       
                         ( 
                         
                           
                             E 
                             stopper 
                           
                           × 
                           δ 
                           ⁢ 
                           
                             t 
                             
                               flange 
                               ⁢ 
                                   
                               top 
                               ⁢ 
                                   
                               surface 
                             
                           
                           × 
                           0.2 
                         
                         ) 
                       
                       × 
                       
                         L 
                         polymer 
                       
                     
                   
                   ≤ 
                   1.2 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     In embodiments, the annular body  162  of the cap skirt  160  may comprise the polymer material having a CTE of greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1  or even greater than or equal to 400×10 −7  K −1 , greater than or equal to 500×10 −7  K −1 , or even greater than or equal to 1,00×10 −7  K −1 . Additionally, the annular body  162  of the cap skirt  160  may have a thickness sufficient so that the ratio of the stiffness of the annular body  162  of the cap skirt  160  to the stiffness of the compressed stopper  106  at the glass transition temperature T g  of the stopper  106  is greater than or equal to 0.7. In embodiments, the annular body  162  may have a radial thickness t CS  of greater than 0.19 mm, such as greater than or equal to 0.20 mm, greater than or equal to 0.21 mm, greater than or equal to 0.25 mm, greater than or equal to 0.50 mm, or even greater than or equal to 1 mm. 
     It has also been found that increasing the stiffness of the cap  108  by itself can also increase the seal pressure and decrease the probability of CCI failure independent of increasing the CTE of the material comprising the cap  108 . Referring now to  FIG.  12   , the contact area (y-axis) between the stopper  106  and the upper sealing surface  110  as a function of temperature (x-axis) is graphically depicted for cap skirts 160 having constant CTE of 255×10 −7  K −1  at 20° C. and increasing stiffness. In  FIG.  12   , the line indicated by reference number 1202 provides data for a typical cap skirt consisting of aluminum metal and having a thickness of 0.19 mm. For reference number  1204 , the stiffness of cap skirt  160  was increased by 1.5 times the stiffness of the typical cap skirt of reference number  1202 , while keeping the CTE constant. For reference number  1206 , the stiffness was increased by 2 times the stiffness of the typical cap skirt (ref no.  1202 ), and for reference number  1208 , the stiffness was increased by 4 times the stiffness of the typical cap skirt (ref. no.  1202 ). The CTE was held constant. As shown in  FIG.  12   , as the stiffness of the cap skirt  160  increases, the contact area between the stopper  106  and the upper sealing surface  110  increases at temperatures less than about −100° C. At a temperature of −180° C., increasing the stiffness by a factor of 2 nearly doubles the contact area between the stopper  106  and the upper sealing surface  110 . Thus, the contact area between the stopper  106  and the upper sealing surface  110  can be increased at temperatures less than −100° C., −110° C., −120° C., −150° C., or even −180° C. by increasing the stiffness of the cap skirt  160 , thereby decreasing the probability of CCI failure at these reduced storage temperatures. 
     Referring again to  FIG.  5   , in embodiments, at least a portion of or all of the cap skirt  160  may have a stiffness that is greater than or equal to 2 times a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. In embodiments, at least a portion of or all of the annular body  162  of the cap skirt  160  may have a stiffness that is greater than or equal to 2 times a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. The stiffness of the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , can be increased by increasing the Young&#39;s modulus of the material comprising the cap skirt  160 , changing the geometry of the cap skirt  160  (e.g., increasing the thickness t CS  of the annular body  162 ), or both. 
     The Young&#39;s modulus of the cap skirt  160  can be increased by constructing at least a portion of or all of the cap skirt  160 , in particular at least a portion of the annular body  162  of the cap skirt  160 , from a metal or metal alloy having a Young&#39;s modulus greater than the Young&#39;s modulus of aluminum metal or an aluminum alloy. In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may comprise a metal or metal alloy having a Young&#39;s modulus that is greater than or equal to 2 times the Young&#39;s modulus of a metal consisting of aluminum or an aluminum-based alloy, where an aluminum-based alloy refers to a metal alloy comprising at least 50 wt. % aluminum. Aluminum and aluminum-based alloys have Young&#39;s moduli in the range of from 67 GPa to 73 GPa. In embodiments, the cap skirt  160 , in particular the annular body  162  of the cap skirt  160 , may comprise a metal or metal alloy having a Young&#39;s modulus that is greater than or equal to 134 GPa, greater than or equal to 140 GPa, greater than or equal to 145 GPa, greater than or equal to 150 GPA, or even greater than or equal to 160 GPa. Examples of suitable metals may include but are not limited to iron, nickel, steel, and alloys of iron, nickel, or steel. In embodiments, the cap skirt  162  and crimp region  164  may be constructed of the same metal or metal alloy having a Young&#39;s modulus greater than or equal to 134 GPa. In other embodiments, the cap skirt  162  can be the metal or metal alloy having Young&#39;s modulus greater than or equal to 134 GPa, and the crimp region  164  can comprise an aluminum or aluminum-based alloy having a lesser Young&#39;s modulus. 
     Referring again to  FIG.  14   , the stiffness of the cap skirt  160 , or the annular body  162  of the cap skirt  160 , can also be increased by modifying the geometry of the annular body  162 . For constant axial length L of the annular body  162 , the stiffness of the annular body  162  of the cap skirt  160  can be increased by increasing the radial thickness t CS  of at least a portion of or all of the annular body  162  of the cap skirt  160 . In embodiments, at least a portion of or all of the annular body  162  of the cap skirt  160  may have a radial thickness t CS  that is greater than a radial thickness of a typical commercially available cap skirt comprising aluminum metal so that the stiffness of the annular body  162  of the cap skirt  160  is greater than or equal to 2 times the stiffness of the typical commercially-available cap skirt comprising aluminum metal. In embodiments, at least a portion of or all of the annular body  162  of the cap skirt  160  may have a radial thickness t CS  that is greater than or equal to 2 1/3  times the radial thickness of a typical commercially-available cap skirt comprising aluminum metal. In embodiments, at least a portion of or all of the annular body  162  of the cap skirt  160  may have a radial thickness t CS  that is greater than or equal to 0.22 mm, greater than or equal to 0.23 mm, greater than or equal to 0.24 mm, greater than or equal to 0.25 mm, or even greater than or equal to 0.30 mm. 
     In embodiments, the stiffness of the cap skirt  160  may be increased by both increasing the Young&#39;s modulus of the material comprising the annular body  162  of the cap skirt  160  and increasing the radial thickness t CS  of at least a portion of the annular body  162  of the cap skirt  160 . Thus, a combination of an increase in Young&#39;s modulus and an increase in radial thickness t CS  of the annular body  162  of the cap skirt  160  can increase the stiffness of the cap skirt  160  to greater than or equal to 2 times the a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. In embodiments, the annular body  162  of the cap skirt  160  may comprise a material having a Young&#39;s modulus of greater than 73 GPa, such as from greater than 73 GPa to 140 GPa or even greater than 140 GPa, and at least a portion of the annular body  162  of the cap skirt  160  may have a radial thickness t CS  of greater than 0.19 mm, greater than or equal to 20 mm, greater than or equal to 21 mm, or even greater than or equal to 22 mm, such that the combination of Young&#39;s modulus and radial thickness t CS  of the annular body  162  result in the cap skirt  160  having a stiffness greater than or equal to 2 times the a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. 
     Additionally, the inventors of the present disclosure have also discovered that increasing the CTE of the cap skirt  160  in combination with increasing the stiffness of the cap skirt  160  produces a synergistic effect that further improves the contact area and seal pressure between the stopper  106  and the upper sealing surface  110  of the flange  126  beyond the contact area and seal pressure that would be achievable with only one of increasing the CTE or increasing the stiffness. Referring now to  FIG.  13   , the contact area (y-axis) between the stopper  106  and the upper sealing surface  110  as a function of temperature (x-axis) for sealed glass containers  100  having cap skirts  160  with different CTE and stiffness is graphically depicted. In  FIG.  13   , the line indicated by reference number  1302  shows the contact area as a function of temperature for a sealed glass container  102  for which the cap skirt  160  has a CTE of 236×10 −7  K − &#39; and a first stiffness. The first stiffness corresponds to the stiffness of a cap skirt consisting of aluminum and having a radial thickness of 0.19 mm. The cap skirt of reference number  1302  had a contact area of less than 10 mm 2  at temperatures less than −120° C. For reference number  1304 , the stiffness of the cap skirt  160  was increased to a stiffness of 1.5 times the first stiffness. As shown in  FIG.  13   , increasing the stiffness by 1.5 times the first stiffness (ref. no.  1304 ) resulted in an increase in the contact area, but the contact area was still around 12 mm 2 . For reference number  1306 , the cap skirt  160  had a stiffness equal to the first stiffness (same as reference no.  1302 ), but the CTE of the cap skirt  160  was increased to 352×10 −7  K −1 . As shown in  FIG.  13   , keeping the stiffness the same and only increasing the CTE of the cap skirt  160  increased the contact area to a range of between 25 mm 2  and 30 mm 2  at temperatures between −120° C. and −180° C. 
     For reference number 1308, the CTE of the cap skirt  160  was increased to 352×10 −7  K −1  and the stiffness of the cap skirt  160  was increased to 1.5 times the first stiffness. As shown in  FIG.  13   , increasing both the CTE and stiffness (ref no.  1308 ) resulted in the contact area increasing to between 50 mm 2  and 62 mm 2  at temperatures between -120° C. and −180° C., which was over 2 times the increase in contact area achieved by increasing the CTE to 352×10 −7  K −1  alone without changing the stiffness. The results are unexpected because the observed increase in contact area resulting from increasing the CTE and stiffness is substantially greater than merely adding the individual effects of increasing the CTE (ref. no.  1304 ) and increasing the stiffness (ref no.  1306 ). Merely adding the effects shown for reference numbers  1304  and  1306  would be expected to result in a contact area in a range of 35 mm 2  to 38 mm 2  at temperatures of from −120° C. to −180° C. However, increasing the CTE and the stiffness of the cap skirt  160  simultaneously (ref no.  1308 ) resulted in a contact area of from 55 mm 2  to 62 mm 2  over the temperature range of −120° C. to −180° C., which is almost two times the contact area expected by just adding the individual effects (i.e., adding the difference between  1304  and  1302  to the difference between  1306  and  1302 ). 
     In embodiments, the cap skirt  160  may have a CTE of greater than 255×10 −7  K −1 , greater than or equal to 280×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1  and may have a stiffness that is greater than a stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. The stiffness of the cap skirt  160  may be greater than or equal to 1.2 times, greater than or equal to 1.3 times, greater than or equal to 1.4 times, greater than or equal to 1.5 times, or greater than or equal to 2.0 times the stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. 
     As previously discussed, the stiffness of the cap skirt  160  may be increased by increasing the Young&#39;s modulus of the annular body  162  of the cap skirt  160 , increasing the thickness of at least a portion of the annular body  162  of the cap skirt  160 , or both. The annular body  162  of the cap skirt  160  may have any of the features, materials, or characteristics previously described herein resulting in both increased CTE and increased stiffness of the cap skirt  160  compared to typical commercially-available cap skirts consisting of aluminum and having a thickness of 0.19 mm and identical axial length. In embodiments, the cap skirt  160  may comprise the annular body  162  comprising a material having a CTE greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 , and a Young&#39;s modulus greater than 73 GPa, greater than or equal to 80 GPa, greater than or equal to 90 GPa, greater than or equal to 100 GPa, greater than or equal to 120 GPa, or even greater than or equal to 140 GPa. In embodiments, the cap skirt  160  may include the annular body  162  comprising a material having a CTE greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 , and at least a portion of the annular body  162  may have a radial thickness t CS  that is greater than or equal to 0.20 mm, greater than or equal to 0.21 mm, greater than or equal to 0.22 mm, greater than or equal to 0.23 mm, greater than or equal to 0.24 mm, greater than or equal to 0.25 mm, greater than or equal to 0.50 mm, or even greater than or equal to 1.0 mm. In embodiments, the cap skirt  160  may comprise the annular body  162  comprising: (1) a material having a CTE greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 , and a Young&#39;s modulus greater than 73 GPa, greater than or equal to 80 GPa, greater than or equal to 90 GPa, greater than or equal to 100 GPa, greater than or equal to 120 GPa, or even greater than or equal to 140 GPa; and (2) at least a portion of the annular body  162  may have a radial thickness t CS  that is greater than or equal to 0.20 mm, greater than or equal to 0.21 mm, greater than or equal to 0.22 mm, greater than or equal to 0.23 mm, greater than or equal to 0.24 mm, greater than or equal to 0.25 mm, greater than or equal to 0.5 mm, or even greater than or equal to 1.0 mm. 
     Referring again to  FIG.  14   , the cap  108  may have a cap skirt  160  comprising a polymer-metal composite structure and a top cover  170 . At least a portion of the annular body  162  of the cap skirt  160  may comprise a polymer material having CTE greater than 255×10 −7  K −1 , greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 , and the crimp region 162 may comprises a crimpable metal, such as aluminum metal or an aluminum metal alloy. The annular body  162  of the cap skirt  160  may have a reinforced region 180 where the radial thickness t CS  is greater than or equal to 0.20 mm, greater than or equal to 0.21 mm, greater than or equal to 0.22 mm, greater than or equal to 0.23 mm, greater than or equal to 0.24 mm, greater than or equal to 0.25 mm, or even greater than or equal to 0.30 mm. The reinforced region  180  may comprise at portion of or all of the annular body  162 . In embodiments, the reinforced region  180  may comprise at least 30%, at least 40%, at least 50%, at least 60%, or even at least 70% of the axial length L of the annular body  162  of the cap skirt  160 . The radial thickness t CS  of the annular body  162  may increase the stiffness of the cap skirt  160  to a stiffness that is greater than or equal to 1.2 times, greater than or equal to 1.3 times, greater than or equal to 1.4 times, greater than or equal to 1.5 times, or greater than or equal to 2.0 times the stiffness of a comparable cap skirt annular body consisting of aluminum metal and having a radial thickness of 0.19 mm and identical axial length. The cap skirt  160  may have both increased CTE and increased stiffness, which may enable the cap skirt  160  to maintain a contact area and seal pressure between the stopper  106  and the upper sealing surface  110  of the glass container  102  when the sealed glass container  100  is cooled to temperatures less than −80° C. 
     As shown in  FIG.  14   , the cap  108  may have the top cover  170  that is separate from the cap skirt  160  and removeably attachable to the cap skirt  160 . In such embodiments, the top cover  170  may be removed from the cap skirt  160  prior to use of the sealed glass container  100 , such as to provide access to the stopper  106  using a syringe or other device to withdraw the contents of the sealed glass container  100 . The top cover  170  may be engageable with the attachment flange  166  of the cap skirt  160 . In embodiments, the top cover  170  may include a slot  172  shaped to receive the attachment flange  166 , where engagement of the attachment flange  166  with the slot  172  couples the top cover  170  to the cap skirt  160 . In embodiments, the annular body  162  of the cap skirt  160  may have a notch  182  positioned to receive an end  174  of the top cover  170 . 
     The top cover  170  may comprise a polymer material, such as a polymer having a CTE greater than 255×10 −7  K −1 , greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1  or even greater than or equal to 500×10 −7  K −1 . In embodiments, the top cover 170 may be constructed of the same polymer material as the annular body  162  of the cap skirt  160 . In embodiments, the top cover  170  may be a material different from the annular body  162  of the cap skirt  160 . 
     Referring now to  FIG.  15   , in embodiments, the cap  108  may comprise a unitary structure in which the cap skirt  160  and top cover ζare integrally formed together to produce the single unitary structure. In embodiments, the reinforced region  180  of the annular body  162  may extend from the crimp region  164  all the way to the top  171  of the top cover  170  portion of the cap  108 . The cap  108  comprising the cap skirt  160  and top cover  170  integrally formed into a unitary structure may further comprise the crimp region  164  extending downwardly (e.g., generally in the −Z direction of the coordinate axis in  FIG.  15   ) from the cap skirt  160  portion of the cap  108 . The annular body  162  of the cap skirt  160  and the top cover  170  portion of the cap  108  may comprise a polymer material having a CTE greater than 255×10 −7  K −1 , greater than or equal to 260×10 −7  K −1 , greater than or equal to 300×10 −7  K −1 , greater than or equal to 350×10 −7  K −1 , even greater than or equal to 400×10 −7  K −1 , or even greater than or equal to 500×10 −7  K −1 . 
     The annular body  162  of the cap  108  may have any of the features, materials, or dimensions previously described herein for the annular body  162 . In embodiments, the annular body  162  of the cap  108  may have an increased CTE, increased stiffness, or both according to any of the embodiments previously described herein. The increased CTE, increased stiffness, or both of the annular body  162  of the cap  108  may increase the seal pressure and contact area between the stopper  106  and the upper sealing surface  110  of the flange  126  of the glass container  102 . The increased seal pressure and contact area provided by the caps  108  disclosed herein may reduce the probability of CCI failure. 
     When formed integrally into a unitary structure, the top cover  170  may not be removable from the cap skirt  160  of the cap  108 . In embodiments, the top cover  170  portion of the cap  108  may include an opening  176  extending axially through the top cover  170  portion. The opening  176  may provide access to the stopper  106  enclosed by the cap  108 . Access to the stopper  106  provided by the opening  176  in the top cover  170  portion may enable the contents of the sealed glass container  100  to be removed using a needle or other penetrating device to pierce through the stopper  106  and draw out the contents of the sealed glass container  100  without removing the cap  108  and stopper  106 . The needle or other penetrating device may be passed through the opening  176  in the top cover  170  portion of the cap  108  and then passed through the stopper  106  and into the sealed glass container  100 . The opening  176  in the top cover  170  portion of the cap  108  may be coaxial with the center axis C of the sealed glass container  100 . 
     Referring now to  FIG.  16   , an embodiment of the cap  108  having a cap skirt  160  comprising an annular body  162  having high CTE and high stiffness is schematically depicted. The increased stiffness for the cap  108  in  FIG.  16    is provided by increased radial thickness t CS  of the annular body  162  of the cap skirt  160 . Referring now to  FIGS.  17 A,  17 B, and  17 C , the seal pressure between the stopper  106  and the upper sealing surface  110  of the flange  126  of the glass container  102  for the cap  108  of  FIG.  16    is simulated at different temperatures. The annular body of the cap skirt is constructed of high-density polyethylene (HDPE) having a CTE of 1,264×10 −7  K −1  and a Young&#39;s modulus of only 1 GPa. The stiffness is increased by increasing the thickness of the annular body  162  of the cap skirt  160  from 0.2 mm to 2.14 mm. The seal pressure between the stopper  106  and the upper sealing surface  110  of the flange  126  was simulated at 25° C. ( FIG.  17 A ), −80° C. ( FIG.  17 B ), and −180° C. ( FIG.  17 C ). As shown in  FIGS.  17 A,  17 B, and  17 C , the increased CTE and stiffness of the cap skirt  162  was able to maintain sufficient seal contact area and pressure between the stopper  106  and the upper sealing surface  110  even at temperatures down to −180° C. 
     Referring now to  FIG.  18   , contact area (y-axis) between the upper sealing surface  110  of the flange  126  and the stopper  106  as a function of temperature (x-axis) for a sealed glass container comprising the cap  108  of  FIG.  16    having a CTE of 1264×10 −7  K −1  at 20° C. and thickness of 2.14 mm cooled at a constant cooling rate is shown and compared to the contact area for a sealed glass container comprising a conventional cap constructed of aluminum and having a thickness of 0.2 mm. In  FIG.  18   , reference number  1802  refers to the sealed container comprising the conventional cap constructed of aluminum metal and having a thickness of the annular body of 0.2 mm. Reference number  1804  refers to the sealed glass container comprising the cap of  FIG.  16    having an HDPE cap skirt with a CTE of 1264×10 −7  K −1  at 20° C., a Young&#39;s modulus of 1 GPa, and a thickness of 2.14 mm. As shown in  FIG.  18   , the contact area for the sealed glass container comprising the cap of  FIG.  16    having greater CTE and stiffness provided substantially greater contact area compared to the sealed glass container comprising conventional cap constructed of aluminum at temperatures less than −80° C. In particular, the cap of  FIG.  16    ( 1804 ) provided nearly 10 times the contact area compared to the conventional aluminum cap ( 1802 ) at temperatures less than −80° C. 
     The caps  108  disclosed herein having increased CTE, increased stiffness, or both may increase the seal pressure and contact area between the stopper  106  and the upper sealing surface  110  of the flange  126  of the glass container  102 . The increased seal pressure and contact area provided by the caps  108  disclosed herein may reduce the probability of CCI failure. In particular, the caps  108  disclosed herein may enable the sealed glass containers  100  to maintain a helium leakage rate of the sealed glass container  100  of less than or equal to 1.4×10 −6  cm 3 /s as the sealed pharmaceutical container is cooled to a temperature of less than or equal to −45° C., less than or equal to −80° C., less than or equal to −100° C., less than or equal to −120° C., or even less than or equal to −180° C. 
     The caps  108  disclosed herein may be utilized in combination with other features of the glass container  102 , stopper  106 , or both to further reduce the probability of CCI failure at low storage temperatures of less than −80° C. Referring again to  FIGS.  1 - 4   , the structure of the glass container  102  may be modified to deviate from existing glass containers to provide greater compression of the stopper  106  during the process of crimping the cap  108 . Referring again to  FIG.  2   , the upper sealing surface  110  may include an inclined sealing surface  140 . The inclined sealing surface  140  extends between the outer surface  134  of the flange  126  and the inner surface  114  of the glass container  102 . The inclined sealing surface  140  may extends at an angle  150  to a plane  152  extending through an end  154  of the opening  105 . The plane  152  may be a planar surface that rests on top of the glass container  102  at the opening  105  (e.g., that rests on peaks of the inclined sealing surface  140 ) and is perpendicular to the center axis C of the glass container  102  (e.g., in the X-direction depicted in  FIG.  1   ). 
     The angle  150 , as described herein, may be referred to as a “flange angle.” Flange angles relative to the plane  152  may be measured in a variety of different ways. For example, in embodiments, to determine an extension direction for the inclined sealing surface  140 , an image may be captured of the glass container  102 , and image processing techniques may be used to determine the angle  150  of the inclined sealing surface  140  (relative to the plane  152 ). In embodiments, the extension direction of the inclined sealing surface  140  is measured via finding a plane that extends between a peak of the inclined sealing surface  140  (e.g., having the greatest distance in the +/-Z direction from the underside surface  132 ) and a second highest point on the inclined sealing surface  140  (e.g., the extension direction of the inclined sealing surface  140  is measured via a plane that rests on the peak of the inclined sealing surface and another point of the inclined sealing surface  140  that is lower than the peak relative to the plane  152 ). In embodiments, the extension direction of the inclined sealing surface  140  is measured via connecting points on the inclined sealing surface  140  that are a predetermined distance (e.g., 0.1 mm, 0.2 mm, 0.5 mm, 1.0 mm, etc.) outward from the inner surface  114  and inward of the outer surface  134  (e.g., the points may be taken at a uniform distribution of spatial points extending between the inner surface  114  and the outer surface  134 ). In embodiments, the extension direction of the inclined sealing surface  140  is measured by curve fitting a linear plane to a plurality of different points distributed throughout the entirety of the inclined sealing surface  140 . 
     In embodiments, the angle  150  may be greater than 5 degrees and less than or equal to 45 degrees (e.g., greater than 5 degrees and less than or equal to 40 degrees, greater than 5 degrees and less than or equal to 40 degrees, greater than 5 degrees and less than or equal to 30 degrees, greater than 5 degrees and less than or equal to 20 degrees, greater than 5 degrees and less than or equal to 10 degrees). In embodiments, the angle  150  is substantially uniform around a circumference of the glass container  102  (e.g., when measured at a plurality of azimuthal orientations, each of the measurements may be within 0.5 degrees of one another). In existing glass containers, the angle  150  is typically around 3 degrees. As such, in the glass container  102 , the inclination of the upper sealing surface  110  relative to the plane  152  is increased by at least 50% over existing glass containers. 
     The greater inclination of the upper sealing surface  110  may increase stopper compression at low storage temperatures, thereby increasing the sealing pressure between the stopper  106  and the upper sealing surface  110  of the flange  126 . The angle  150  may create a compression gradient within the stopper  106  as a result of crimping the cap  108 . For example, in embodiments, a compression of the stopper  106  may increase with increasing radial distance from the outer surface  134  such that the compression of the stopper is greater closer to the inner surface  114 . Such greater compression with proximity to the inner surface  114  may prevent gaps from forming in the seal as the stopper  106  shrinks with cooling. The stopper  106  is compressed to a greater extent proximate to the opening  105  than at peripheral regions of the stopper  106  disposed near the outer surface  134  of the flange  126 . Such greater compression results in a greater compression of the stopper  106  using the same crimping process, providing a higher tolerance for shrinkage of the stopper  106 . Additionally, the inclined sealing surface  140  reduces the term L i,stopper  in Equation 3 above proximate to the opening  105 . This reduces the amount of shrinkage of the cap  108  that is necessary to maintain the relationship of Equation 1 herein. 
     Referring again to  FIG.  3   , in embodiments, the upper sealing surface  110  may extend in the plane  152  extending through the end  154  of the opening  105  in the glass container  102 . In embodiments, the upper sealing surface  110  may extend substantially perpendicular (e.g., at an angle greater than or equal to 89.5 degrees and less than or equal to 90.5 degrees) to the center axis C of the glass container  102 . Such an upper sealing surface  110  may increase the contact area between the stopper  106  (see  FIG.  1 A ) and the upper sealing surface  110  and may increase the probability of maintaining integrity of the seal. 
     In embodiments, various additional characteristics of the upper sealing surface  110  and/or the inclined sealing surface  140  depicted in  FIG.  2    may be tailored for maintaining a seal at storage temperatures less than or equal to −80° C. For example, in embodiments, the upper sealing surface  110  may comprise a surface roughness (e.g., Ra value) that is less than or equal to a threshold value (e.g., 0.1 μm, 50 nm, etc.). Such a low surface roughness may beneficially prevent the stopper  106  from pulling away from the upper sealing surface  110  upon cooling. In embodiments, the upper sealing surface  110  may be substantially free of defects (e.g., folds, bumps, ridges, etc.). Such defects may lead to gaps forming at the interface between the upper sealing surface  110  and the stopper  106 , thereby reducing seal quality. A flatness of the inclined sealing surface  140  may be maintained within a threshold value to facilitate adherence between the stopper  106  and the upper sealing surface  110 . 
     In embodiments, the upper sealing surface  110  comprises a surface roughness (e.g., Sa value) that is greater than or equal to a threshold value (e.g., 3 μm, 5 μm, 10 μm) to increase friction at the upper sealing surface  110  between the glass container  102  and the stopper  106 . In such embodiments, the surface roughness of the upper sealing surface  110  may be relatively uniform throughout the entirety thereof. For example, Sa values of the upper sealing surface  110  throughout a plurality of different measurement windows (e.g., 100 μm by 100 μm) may vary by less than or equal 0.1 p.m. In embodiments, the roughness of the upper sealing surface  110  may be determined based at least in part on properties (e.g., surface roughness) of the stopper  106 . In embodiments, the roughness of the upper sealing surface  110  may approximately equal a difference in shrinkage between the metal-containing cap  108  and the combination of the flange  126  and stopper  106 . For example, in embodiments, the surface roughness of the upper sealing surface  110  may be within a threshold value of the estimated shrinkage difference between the cap  108  and the combination of the stopper  106  and flange  126 . Providing such a surface roughness may ensure at least some contact between the upper sealing surface  110  and the stopper  106  after cooling. 
     For example, in embodiments, a flange thickness  158  (e.g. distance between the upper sealing surface  110  and the underside surface  132 ) may be increased over existing glass containers. In such embodiments, if the stopper  106  and crimping process of the cap  108  is un-modified, the proportion of the combined height  138  of material enclosed by the cap  108  containing stopper  106  is reduced, thereby reducing the shrinkage of the cap  108  needed to satisfy Equation 1 described herein. Alternatively or additionally, the size of the stopper  106  (e.g., in terms of thickness of the sealing portion  119 ) may be reduced. In embodiments, the flange height  158  is greater than or equal to 4.0 mm and constitutes at least 61% of the combined height  138 . 
     The features of the cap  108  disclosed herein may also be used in combination with compositional changes to the stopper  106  to further increase the seal pressure and contact area and decrease the probability of CCI failure. In embodiments, the composition of the stopper  106  may be chosen to lower the CTE or glass transition temperature thereof. Choosing such compositions for the stopper  106  may lower the shrinkage thereof and therefore help maintain compression of the stopper  106  via the cap  108 . In embodiments, the polymer formulation of the stopper  106  may be chosen (or additions may be added to the stopper  106 ) such that the glass transition temperature of the stopper  106  is less than or equal to −45° C., less than or equal to −70° C., less than or equal to −75° C., less than or equal to −80° C., or even less than or equal to −85° C. In embodiments, the stopper  106  may comprise a polymer composition that has a glass transition temperature that is greater than or equal to −70° C. and less than or equal to −45° C. In embodiments, the glass transition temperature of the stopper  106  may be lowered to below a desired storage temperature of the sealed glass container  100  (e.g., to less than or equal to dry ice storage temperatures around −80° C.) such that the stopper  106  retains elasticity, creating the seal at the upper sealing surface  110 . In embodiments, the stopper  106  may comprise one or more low T g  elastomeric materials such as Polybutadienes, silicones, fluorosilicones, nitrites, and EPDM elastomers (e.g., PDMS), or any combination thereof. In embodiments the elastomeric material may comprise a material having a glass transition temperature that is less than or equal to −100° C. 
     In embodiments, the stopper  106  may comprise a polymer-based composite material having a lower CTE than typically used rubber materials. In embodiments, the stopper  106  may comprise a rubber-filler mixture. For example, in embodiments, the stopper  106  may comprise a polymer or rubber material and up to 15% by volume of filler material. In embodiments, the stopper  106  may comprise less than or equal to 40 wt. % filler material (e.g., less than or equal to 30 wt. % filler material). More than 40 wt. % filler material may diminish seal quality by lowering the elasticity of the stopper  106 . The filler material may have a CTE that is less than that of the rubber out of which stoppers are typically constructed (e.g., less than or equal to 50×10 −7  K −1 , less than or equal to 20×10 −7  K −1 , less than or equal to 10×10 −7  K −1 , less than or equal to 5×10 −7  K −1 ). In embodiments, the filler may comprise silicon. For example, in embodiments, the filler material may comprise SiO 2  glass particles having a particle size that is greater than or equal to 10 nm and less than or equal to 100 nm. In embodiments, the SiO 2  glass particles may be functionalized with oranosilanes to tune the particle dispersion state within the elastomeric material of the stopper  106 . In embodiments, the filler material may comprise a silicate (e.g., cordierite, b-eucryptite, b-spodumene). In embodiments, the filler material may be a high melting point metal (e.g., Ir, W, Ti, Si). In embodiments, the filler material may comprise Mg 2 PO 4 . In embodiments, the filler material may comprises an oxide, such as SiO 2 , Ti-doped SiO 2 , ZrW 2 O 8 , or other ceramics in the AM 2 O 8  family. In embodiments, the filler material may comprise any other suitable material with a relatively low or negative CTE. In embodiments, the CTE of the stopper  106  containing the filler material may be less than or equal to 300×10 −7  K −1  (e.g., less than or equal to 290×10 −7  K −1 , less than or equal to 280×10 −7  K −1 , less than or equal to 270×10 −7  K −1 ). By adding the filler material described herein to the stopper  106 , the CTE of the stopper  106  may be reduced relative to the CTE of the metal cap  108 , thereby reducing the likelihood of decompression of the stopper  106  when the sealed glass container  100  is cooled to storage temperatures that are less than or equal to −80° C. 
     It should be appreciated that any combination of the above-described approaches (e.g., increasing the CTE and/or stiffness of the cap  108 , lowering the CTE and/or T g  of the stopper  106 , structurally modifying the glass container  102  in any of the ways described herein) may be used in the sealed glass container  100 . In embodiments, both cap  108  comprising a high CTE greater than or equal to 260×10 −7  K −1  and/or high stiffness of greater than or equal to 140 GPa (e.g., constructed of a polymer-aluminum composite) and low CTE stopper  106  (e.g., constructed of a rubber-SiO 2  composite) may be used. In such embodiments, given that the shrinkage differential between the metal-containing cap  108  and the stopper  106  is reduced by composition formulation, modification of the structure of the glass container  102  may be avoided. 
     The caps  108  disclosed herein may be incorporated into a method for sealing a glass container, such as a method of sealing a sealed pharmaceutical container. Referring again to  FIG.  5   , in embodiments, a method of sealing a sealed pharmaceutical container may include providing the glass container  102  comprising the shoulder  130 , the neck  128  extending from the shoulder  130 , and the flange  126  extending from the neck  128 . The glass container  102  may be a pharmaceutical container and may include any of the features, compositions, or characteristics previously described herein for the glass container  102 . The flange  126  may include an underside surface  132  extending from the neck  128 , an outer surface  134  extending from the underside surface  132  and defining an outer diameter of the flange  126 , and an upper sealing surface  110  extending between the outer surface  132  and the inner surface  114  of the sealed glass container  100 . The inner surface  114  defines the opening  105  in the glass container  102 . The methods may further include inserting a pharmaceutical composition into the glass container  102  and providing the sealing assembly  104  comprising the stopper  106  and the cap  108 . The stopper  106  and cap  108  may have any of the features, materials, or characteristics previously described herein for the stopper  106  and cap  108 , respectively. 
     The methods may further include inserting the stopper  106  into the opening  105  in the glass container  102  so that the stopper  106  extends over the upper sealing surface  110  of the flange  126  and covers the opening  105 . The method may further include crimping the cap  108  over the stopper  106  and against the flange  126  to thereby compress the stopper  106  against the upper sealing surface  110 . The methods may further include cooling the sealed glass container  100  to a temperature of less than or equal to −45° C., such as less than or equal to −80° C., less than or equal to −100° C., less than or equal to −120° C., or even less than or equal to −180° C. After the cooling of the sealed glass container  100 , the compression is maintained on the upper sealing surface  110  such that a helium leakage rate of the sealed glass container  100  is less than or equal to 1.4×10 −6  cm 3 /s at the temperature. 
     Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation, and; the number or type of embodiments described in the specification. 
     It will be apparent to those skilled in the art that various modifications and variations can be made to the embodiments described herein without departing from the spirit and scope of the claimed subject matter. Thus, it is intended that the specification cover the modifications and variations of the various embodiments described herein provided such modification and variations come within the scope of the appended claims and their equivalents.